The world No. 1 and top-seeded Federer defeated American Sam Querrey 6-4, 6-4, 6-3 in a first-round match that lasted an hour and 35 minutes. Federer had five service breaks.
The 26-year-old Federer, who has won 12 Grand Slam tournaments, has yet to take the French crown. He has lost to Spaniard Rafael Nadal in the last two finals.
"The first round of a slam is always hard to get through," Federer said after defeating Querrey.
Eleventh-seeded Tomas Berdych of the Czech Republic also advanced, crushing Australian Robert Smeets 6-1, 6-0, 6-1.Spaniard Tommy Rebredo, seeded 12th, eliminated former French Open runner-up Guillermo Coria 5-7, 6-4, 6-1, 6-4. .
Among seeds who had their matches postponed until Tuesday were three-time defending champion Nadal, seeded No. 2, and No. 9 Stanislas Wawrinka.