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

    <schemaVersion>X0508</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2026-01-06</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001835856</issuerCik>
        <issuerName>Better Home &amp; Finance Holding Co</issuerName>
        <issuerTradingSymbol>BETR</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0002022869</rptOwnerCik>
            <rptOwnerName>Smith Chad M.</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O BETTER HOME &amp; FINANCE HOLDING CO</rptOwnerStreet1>
            <rptOwnerStreet2>1 WORLD TRADE CENTER, 80TH FLOOR SUITE A</rptOwnerStreet2>
            <rptOwnerCity>NEW YORK</rptOwnerCity>
            <rptOwnerState>NY</rptOwnerState>
            <rptOwnerZipCode>10013</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>Pres &amp; COO,  Better Mortgage</officerTitle>
        </reportingOwnerRelationship>
    </reportingOwner>

    <aff10b5One>1</aff10b5One>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Class A Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2026-01-06</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>2843</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>35.1451</value>
                    <footnoteId id="F1"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>27590</value>
                    <footnoteId id="F2"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>By Trust</value>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <derivativeTable></derivativeTable>

    <footnotes>
        <footnote id="F1">The price reported in Column 4 is a weighted average price for shares sold in multiple transactions. The sale prices range from $35.00 to $35.60 per share. The reporting person has provided to the issuer, and undertakes to provide to the staff of the Securities and Exchange Commission or any security holder of the issuer, upon request, full information regarding the number of shares sold at each separate price within the range.</footnote>
        <footnote id="F2">The shares of Class A Common Stock held by the reporting person prior to the transaction reported herein reflect a transfer of 2,843 shares previously reported as directly held by the reporting person to the reporting person's Trust, which transfer of shares to the Trust was a change in form of ownership in accordance Rule 16a-13.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Andrew Holt, Attorney-in-Fact</signatureName>
        <signatureDate>2026-01-08</signatureDate>
    </ownerSignature>
</ownershipDocument>
