Sharapova, the No. 1 seed in Paris, had little trouble getting past Chanelle Scheepers 6-3, 6-1. Sharapova won 60 percent of the points in the match and had six breaks in eight receiving games.
She did lose her serve twice but still took nearly two-thirds of the points on serve.
Goerges, seeded sixth, topped Petra Cetkovska 6-1, 6-4 in just more than an hour. She suffered a break early in the second set but won five of the last six games to finish off the match.
All of the other matches Wednesday were in the first round. Given a rash of injuries and upsets, only four of the nine seeded players made it out of the opening round. That includes Sharapova and second-seeded Marion Bartoli, who had first-round byes.
Seventh-seeded Roberta Vinci was among those who advanced as she beat Simona Halep 6-4, 6-4 with two breaks in each set. However, Pauline Parmentier eliminated eighth-seeded Anabel Medina-Garrigues 2-6, 6-3, 6-3. Parmentier had a total of five breaks in the last two sets.
Other players to move into the second round Wednesday were Monica Niculescu, Yanina Wickmayer, Christina McHale, Klara Zakopalova and Bethanie Mattek-Sands.