The 2002 and 2013 champion, and 19-time major winner, next faces Anna-Lena Friedsam of Germany.
Williams has now won 58 of her 59 career first-round matches at the majors.
Canadian sixth seed Bouchard, a semi-finalist in 2014, crashed out at the hands of France's Kristina Mladenovic.
Bouchard went down 6-4, 6-4 to the world number 44, her eighth defeat in her last nine matches.
Mladenovic, 22, goes on to face Danka Kovinic of Montenegro.
Also going out was Bulgarian 10th seed Dimitrov who suffered his second successive first-round exit in Paris, losing 7-6 (9-7), 6-2, 6-3 to Jack Sock of the United States.
Wimbledon champion and fourth seed Petra Kvitova needed two and a half hours to see off New Zealand's world number 80 Marina Erakovic 6-4, 3-6, 6-4, getting broken six times and committing 47 unforced errors.
The 25-year-old goes on to face Silvia Soler-Espinosa of Spain.
Serbian 25th seed Jelena Jankovic, a three-time semi-finalist, suffered her first opening-round loss in a decade when she went down 6-3, 6-4 to Bulgarian qualifier Sesil Karatantcheva.
Spain's David Ferrer won his 300th claycourt match when he swept past Slovakia's Lukas Lacko 6-1, 6-3, 6-1.
Croatia's Marin Cilic, the ninth-seeded US Open champion, defeated Robin Haase of the Netherlands 6-2, 6-4, 6-2.
Svetlana Kuznetsova, the 2009 champion, beat Dutchwoman Kiki Bertens 6-1, 4-6, 6-2 and will next face 2010 winner Francesca Schiavone of Italy.
Fifth seed and former world number one Caroline Wozniacki won through to the second round, beating Italy's Karin Knapp 6-3, 6-0.
Italian Knapp came into the event having claimed her second career title in Nuremberg last week.
But she was the architect of her own downfall with a total of 50 unforced errors, and Wozniacki now goes on to face Germany's Julia Goerges.