<?xml version="1.0"?>
<ownershipDocument>

    <schemaVersion>X0508</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2025-12-26</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001050441</issuerCik>
        <issuerName>EAGLE BANCORP INC</issuerName>
        <issuerTradingSymbol>EGBN</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001234907</rptOwnerCik>
            <rptOwnerName>RIEL SUSAN G</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O EAGLE BANCORP, INC.</rptOwnerStreet1>
            <rptOwnerStreet2>7500 OLD GEORGETOWN ROAD</rptOwnerStreet2>
            <rptOwnerCity>BETHESDA</rptOwnerCity>
            <rptOwnerState>MD</rptOwnerState>
            <rptOwnerZipCode>20814</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>President &amp; CEO</officerTitle>
        </reportingOwnerRelationship>
    </reportingOwner>

    <aff10b5One>0</aff10b5One>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2025-12-26</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>G</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F1"/>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>1400</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>341379</value>
                    <footnoteId id="F2"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2025-12-26</value>
            </transactionDate>
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                    <value>339979</value>
                </sharesOwnedFollowingTransaction>
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            </ownershipNature>
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        <nonDerivativeTransaction>
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                </transactionShares>
                <transactionPricePerShare>
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                <sharesOwnedFollowingTransaction>
                    <value>338579</value>
                </sharesOwnedFollowingTransaction>
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            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
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        <nonDerivativeTransaction>
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                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2025-12-26</value>
            </transactionDate>
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                <transactionFormType>4</transactionFormType>
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                <directOrIndirectOwnership>
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        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
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                <value>2025-12-26</value>
            </transactionDate>
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                <footnoteId id="F3"/>
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                <transactionShares>
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                <transactionPricePerShare>
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                <transactionAcquiredDisposedCode>
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            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>3490</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>Susan G. Riel and Charles T. Riel Jr. in Trust for Olivia A. Riel</value>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
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            </transactionDate>
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                <footnoteId id="F3"/>
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                <transactionShares>
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                <transactionPricePerShare>
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                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
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            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>335779</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2025-12-26</value>
            </transactionDate>
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                <transactionFormType>4</transactionFormType>
                <transactionCode>G</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F3"/>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>1400</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>3490</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>Susan G. Riel and Charles T. Riel Jr. in Trust for Charlotte A. Riel</value>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2025-12-26</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
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                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F3"/>
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                <transactionShares>
                    <value>1400</value>
                </transactionShares>
                <transactionPricePerShare>
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                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>334379</value>
                </sharesOwnedFollowingTransaction>
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            <ownershipNature>
                <directOrIndirectOwnership>
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        <nonDerivativeTransaction>
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                <value>Common Stock</value>
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            <transactionDate>
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                    <value>1400</value>
                </transactionShares>
                <transactionPricePerShare>
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                <transactionAcquiredDisposedCode>
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                </transactionAcquiredDisposedCode>
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            <postTransactionAmounts>
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                    <value>3490</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>Susan G. Riel and Charles T. Riel Jr. in Trust for Haley G. Sherrill</value>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
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                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
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                <value>Common Stock</value>
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                <directOrIndirectOwnership>
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                <natureOfOwnership>
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                </natureOfOwnership>
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                <directOrIndirectOwnership>
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                <natureOfOwnership>
                    <value>Susan G. Riel and Charles T. Riel Jr. in Trust for Kevin C. Riel</value>
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            <securityTitle>
                <value>Common Stock</value>
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            <transactionDate>
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                <sharesOwnedFollowingTransaction>
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                <directOrIndirectOwnership>
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                <natureOfOwnership>
                    <value>Susan G. Riel and Charles T. Riel Jr. in Trust for Theodore Wyatt Riel</value>
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                    <value>1000</value>
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                <value>Common Stock</value>
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                <sharesOwnedFollowingTransaction>
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                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>Susan G. Riel and Charles T. Riel Jr. in Trust for Charles R. Heinecke Riel</value>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2025-12-26</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>G</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F3"/>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>1000</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>326179</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2025-12-26</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>G</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F3"/>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>1000</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>3090</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>Susan G. Riel and Charles T. Riel Jr. in Trust for Olive S. Heinecke-Riel</value>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <derivativeTable></derivativeTable>

    <footnotes>
        <footnote id="F1">Represents a bona fide gift by the Reporting Person to the Reporting Person's children. The Reporting Person does not retain any beneficial ownership or pecuniary interest over the shares of the Company's Common Stock after effecting the transaction.</footnote>
        <footnote id="F2">The Reporting Person's holdings include 196 shares acquired under the Eagle Bancorp, Inc. 2021 Employee Stock Purchase Plan (the &quot;2021 Plan&quot;) on March 31, 2025; 181 shares acquired under the 2021 Plan on June 30, 2025; and 204 shares acquired under the 2021 Plan on September 30, 2025.</footnote>
        <footnote id="F3">Represents a bona fide gift by the Reporting Person to various trusts, the beneficiaries of which are the Reporting Person's grandchildren. The Reporting Person as co-trustee of each of the trusts retains beneficial ownership over the shares of the Company's Common Stock in the trusts.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>Susan G. Riel</signatureName>
        <signatureDate>2025-12-30</signatureDate>
    </ownerSignature>
</ownershipDocument>
