The top-seeded Roddick, who won the Lyon title in 2005, earned the only break of the match in the second set. Mahut, who also had 18 aces, saved three break points in the first set.
Roddick hurt his knee Monday while playing doubles, but said the injury has healed.
"I did not feel anything this morning, so now everything is fine,'' said Roddick, who next plays either Robby Ginepri or defending champion Sebastien Grosjean.
Roddick is already looking forward to next month's Masters Cup, although he still needs to qualify for the event in Shanghai.
"It's maybe a more open tournament this year,'' the American said. "There's not only Roger (Federer), but others like (Andy) Murray who are playing very well, or (Juan Martin) del Potro. It promises to be a great tournament.''
Also, second-seeded Richard Gasquet of France rallied to beat Santiago Giraldo 5-7, 6-3, 7-6 (3) and advance to the second round.
Gasquet, who has dropped to 15th in the ATP rankings, pressured Giraldo's serve throughout, but could only take two of his seven break-point chances.
Nicolas Lapentti of Ecuador also won, beating sixth-seeded Ivo Karlovic of Croatia 7-6 (4), 6-3, while Fabrice Santoro defeated Fabio Fognini of Italy 6-4, 6-1 and Andreas Seppi of Italy beat David Guez of France 6-2, 7-5.
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