Using an online randomized experiment in the context of the 2019 European elections campaign in France, we study how fact-checking affects sharing of false news on social media. We exposed over 4200 voting-age French to statements on the role of the EU made by the extreme right populist party Rassemblement National. A randomly selected subgroup of experiment participants was also presented with fact-checking of these statements; another subgroup was offered a choice whether to view the fact-checking or not. Then, all participants could choose whether to share the false statements on their Facebook pages. We show that: (i) both imposed and voluntary fact-checking reduced sharing of false statements by more than 25%; (ii) the size of the effect was similar between imposed and voluntary fact-checking; and (iii) each additional click required to share false statements reduced sharing by 75%.