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

    <schemaVersion>X0609</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2026-06-03</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0000708821</issuerCik>
        <issuerName>PAR TECHNOLOGY CORP</issuerName>
        <issuerTradingSymbol>PAR</issuerTradingSymbol>
        <issuerForeignTradingSymbol></issuerForeignTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001968116</rptOwnerCik>
            <rptOwnerName>STEENBERGE MICHAEL ANTHONY</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerNonUSAddressFlag>false</rptOwnerNonUSAddressFlag>
            <rptOwnerStreet1>8383 SENECA TURNPIKE</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>NEW HARTFORD</rptOwnerCity>
            <rptOwnerState>NY</rptOwnerState>
            <rptOwnerZipCode>13413</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>SVP Finance &amp; Transformation</officerTitle>
        </reportingOwnerRelationship>
    </reportingOwner>

    <aff10b5One>1</aff10b5One>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2026-06-03</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>498</value>
                    <footnoteId id="F1"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>14.20</value>
                    <footnoteId id="F2"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>52240</value>
                    <footnoteId id="F3"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <derivativeTable></derivativeTable>

    <footnotes>
        <footnote id="F1">The sales reported on this Form 4 represent shares of Common Stock required to be sold by the Reporting Person to cover tax withholding obligations in connection with the vesting and settlement of a portion of restricted stock units granted on May 13, 2024. These sales are made pursuant to the Company's mandatory, automatic &quot;sell-to-cover&quot; policy as implemented in a Rule 10b5-1 plan adopted on June 3, 2025, and do not represent discretionary trades by the Reporting Person.</footnote>
        <footnote id="F2">The sales price reported in Column 4 is a weighted average price. These shares were sold in multiple transactions at prices ranging from $14.16 to $14.24 inclusive. The Reporting Person undertakes to provide to PAR Technology Corporation, any security holder of PAR Technology Corporation, or the staff of the Securities and Exchange Commission, upon request, full information regarding the number of shares sold at each separate price within the range set forth in this footnote.</footnote>
        <footnote id="F3">Includes 364 shares acquired under the Company's Employee Stock Purchase Plan on June 1, 2026.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Jennifer L Karinen, Attorney-in-fact</signatureName>
        <signatureDate>2026-06-04</signatureDate>
    </ownerSignature>
</ownershipDocument>
