The No. 11-seeded Frenchman defeated Kei Nishikori of Japan 6-3, 6-3 after missing the entire 2009 grass-court season because of a drug suspension. His last match on the surface was against Andy Murray in the 2008 Wimbledon fourth round.
Nishikori was also playing on grass for the first time since Wimbledon in 2008, and his first tour match since March 2009. The Japanese had surgery on his right elbow, and emerged from the second-tier Challenger circuit just last month to compete at Roland Garros.
"It was a good match. I have great sensation and great feelings on the grass court even if I didn't play here last year," said Gasquet, who fought off all five break points he faced in the second set.
Robby Ginepri set up a clash with No. 7-seeded fellow American Sam Querrey by overcoming British wild card James Ward 6-3, 7-5.
Ginepri was made to battle hard in both sets, breaking for 2-0 in the first but then having to fight back from 0-40 to hold for 4-1. He then had to fight off another break point as he served out the set.
Ward broke to lead 4-2 in the second but Ginepri recovered the break when the Briton netted a forehand. Ginepri broke for 6-5 when Ward made another forehand error.
"It was a difficult match," Ginepri said. "I wasn't sure what to expect. He started out a little nervous, I think. He had a break point at 5-3 in the first but I played a good point.
"I just fought hard and hung in there all match. I didn't feel I was hitting the ball particularly well the last three or four days coming into the match, but I live to see another day."
Other seeded winners on the opening day were No. 9 Julien Benneteau over Arnaud Clement 6-2, 6-4, 12th-seeded Michael Llodra of France beating Andrey Golubev of Kazakhstan 6-3, 6-2 and 16th-seeded Denis Istomin who dismissed Jamie Baker of Britain 6-1, 6-4.
The top eight seeds received byes into the second round.
Rafael Nadal will begin his bid to regain his title and heads a field that includes four-time winner Andy Roddick, defending champion Andy Murray and 2008 runner-up Novak Djokovic.
Nadal, again the top-ranked player after winning his fifth French Open title Sunday, was unable to defend his title in 2009 because of a knee injury that also kept him from defending his Wimbledon crown.