Serena Williams, defending champion French Open and top seed, bidding for a fourth Paris title and 22nd Grand Slam crown, starts against Slovakia's Magdalena Rybarikova, the world number 76.
The 27-year-old Slovak has never made it beyond the second round in Paris.
Williams could face 2010 champion Francesca Schiavone of Italy in the third round.
Former world number one and two-time Australian Open winner Victoria Azarenka is a potential quarter-final foe for the 34-year-old American.
Second seed Agnieszka Radwanska is scheduled to face 2014 runner-up Simona Halep in the last eight.
Australian Open champion Angelique Kerber, the third seed, is lined up for a last-eight duel with last year's semi-finalist Timea Bacsinszky.
Wimbledon finalist Garbine Muguruza and US Open runner-up Roberta Vinci is the other potential quarter-final if seedings go to plan.
The women's tournament is missing two-time champion Maria Sharapova who is serving a doping suspension and the injured Caroline Wozniacki.