The 26th-seeded Roddick is 7-10 this season, 0-4 on clay.
Mahut hit more aces than Roddick, 13-8, and broke the American seven times, including in the last game.
Roddick won the 2003 U.S. Open, but only once made it to the fourth round at Roland Garros, in 2009. He's lost in the first round in half of 10 trips, including 2007.
Mahut lost in the first round in Paris eight times in nine previous appearances. He is best known for losing the longest match in tennis history to John Isner, 70-68 in the fifth set at Wimbledon.