How persuasive are “alternative facts,” i.e., false statements by populist politicians, in convincing voters? How effective is fact checking in countervailing alternative facts? We conduct a randomized online experiment to address these questions in the context of the 2017 French presidential election campaign. Marine Le Pen (MLP), the extreme-right candidate who reached the runoff, regularly used alternative facts in support of her policy proposals, to which mainstream media responded with systematic fact checking. We expose randomly selected subgroups of a sample of 2480 voting-age French to quotes from MLP containing fake facts about immigration and/or to facts from official sources. We find that alternative facts are highly persuasive: voters exposed to MLP rhetoric move their policy conclusions and voting intensions toward MLP. Fact checking does nothing to undo these effects despite improving factual knowledge of voters. Being exposed only to official facts also backfires on voting intentions, as it increases political support for MLP, although to a smaller extent than alternative facts, despite moving posteriors about facts toward the truth.