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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2019-07-01</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001071236</issuerCik>
        <issuerName>RED RIVER BANCSHARES INC</issuerName>
        <issuerTradingSymbol>RRBI</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001770059</rptOwnerCik>
            <rptOwnerName>Merrifield Gary A.</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>1412 CENTRE COURT DRIVE, SUITE 402</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>ALEXANDRIA</rptOwnerCity>
            <rptOwnerState>LA</rptOwnerState>
            <rptOwnerZipCode>71301</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>See Remarks</officerTitle>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>COMMON STOCK</value>
            </securityTitle>
            <transactionDate>
                <value>2019-07-01</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F1"/>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>350</value>
                    <footnoteId id="F1"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0.00</value>
                    <footnoteId id="F1"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>3150</value>
                    <footnoteId id="F2"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">Reflects 350 shares of  unvested restricted stock granted to the reporting person on July 1, 2019 that will vest in equal installments on each of the first five anniversaries of the grant date. The reported shares of unvested restricted stock are subject to forfeiture upon the occurrence of certain events specified in the restricted stock grant.</footnote>
        <footnote id="F2">Includes 1,160 shares of unvested restricted stock granted to the reporting person which vest as follows: (i) 340 shares vest on July 1, 2020, (ii) 340 shares vest on July 1, 2021, (iii) 250 shares vest on July 1, 2022, (iv) 160 shares vest on July 1, 2023, and (v) 70 shares vest on July 1, 2024. The reported shares of unvested restricted stock are subject to forfeiture upon the occurrence of certain events specified in the restricted stock grant.</footnote>
    </footnotes>

    <remarks>Senior Vice President and Credit Policy Officer of Red River Bank</remarks>

    <ownerSignature>
        <signatureName>/s/ Amanda W. Barnett, as Attorney-in-Fact</signatureName>
        <signatureDate>2019-07-02</signatureDate>
    </ownerSignature>
</ownershipDocument>
