Protecting American Votes and Elections Act of 2019 This bill addresses the security of federal elections, including by requiring paper ballots, requiring audits of election results, and establishing requirements for election cybersecurity. The bill provides requirements for ballots. Voting systems must use a paper ballot that is verifiable by a voter before being cast and these ballots must be retained for recounts or audits. During a recount, ballots must be counted by hand. States and jurisdictions must perform an audit of an election that must include a manual adjudication of voter intent from some or all of the ballots cast. The audit results must meet specified statistical requirements and must be published before such election is certified. The bill provides a private right of action for any person aggrieved by a violation of voting system or audit requirements. The Election Assistance Commission must provide funds to states to replace paperless voting systems to comply with requirements of the bill, for the acquisition of accessible ballot marking devices for voters with disabilities, for certain ballot design and printing costs, and for certain election audit costs. The bill also directs the Cybersecurity and Infrastructure Security Agency within in the Department of Homeland Security to set mandatory election cybersecurity standards, including those regarding optical scanning devices, ballot marking devices, election management systems, voter registration websites, and election results systems.