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    <periodOfReport>2020-09-28</periodOfReport>

    <notSubjectToSection16>1</notSubjectToSection16>

    <issuer>
        <issuerCik>0001510487</issuerCik>
        <issuerName>Principia Biopharma Inc.</issuerName>
        <issuerTradingSymbol>PRNB</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001506218</rptOwnerCik>
            <rptOwnerName>Hardiman Roy C.</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O PRINCIPIA BIOPHARMA INC.</rptOwnerStreet1>
            <rptOwnerStreet2>220 E. GRAND AVENUE</rptOwnerStreet2>
            <rptOwnerCity>SOUTH SAN FRANCISCO</rptOwnerCity>
            <rptOwnerState>CA</rptOwnerState>
            <rptOwnerZipCode>94080</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
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            <isDirector>0</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>Chief Business Officer</officerTitle>
        </reportingOwnerRelationship>
    </reportingOwner>

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                </transactionShares>
                <transactionPricePerShare>
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                    <value>See footnote</value>
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            <expirationDate>
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            <expirationDate>
                <value>2029-02-28</value>
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                <underlyingSecurityTitle>
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                    <value>60000</value>
                </underlyingSecurityShares>
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            <securityTitle>
                <value>Employee Stock Option (right to buy)</value>
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                <value>67.31</value>
            </conversionOrExercisePrice>
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                <value>2020-09-28</value>
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                <transactionPricePerShare>
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            <expirationDate>
                <value>2030-03-04</value>
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                    <value>Common Stock</value>
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    <footnotes>
        <footnote id="F1">Pursuant to the Agreement and Plan of Merger, dated as of August 16, 2020, by and among Principia Biopharma Inc. (the &quot;Issuer&quot;), Sanofi (&quot;Sanofi&quot;) and Kortex Acquisition Corp. (&quot;Purchaser&quot;) (the &quot;Merger Agreement&quot;), on September 28, 2020, Purchaser merged with and into the Issuer, with the Issuer continuing as the surviving corporation and a wholly owned subsidiary of Sanofi (the &quot;Merger&quot;). At the effective time of the Merger (the &quot;Effective Time&quot;), these shares were canceled in exchange for $100.00 per share in cash, without interest and subject to any applicable withholding taxes.</footnote>
        <footnote id="F2">Shares indirectly held by Roy Hardiman, as a fiduciary for his child, of which the Reporting Person may be deemed to share voting and dispositive power over these shares.</footnote>
        <footnote id="F3">Pursuant to the Merger Agreement, at the Effective Time, each of the unvested and outstanding options was accelerated and became fully vested, and each of the outstanding options was canceled and converted into the right to receive a cash amount equal to the product of (i) the number of shares that are subject to such options, multiplied by (ii) the excess (if any) of (x) $100.00 over (y) the exercise price payable per share under such options.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Christopher Y. Chai, Attorney-in-Fact for Roy Hardiman</signatureName>
        <signatureDate>2020-09-28</signatureDate>
    </ownerSignature>
</ownershipDocument>
