Bartoli, the fifth seed, closed out a straightforward win against the 18-year-old via a fine performance on the opening day of the tournament.
The French player looked set to thrash Robson in the second set as she roared into a 4-0 lead but the Brit, who took silver in the mixed doubles alongside Andy Murray at the London Olympics, reeled off three games in succession.
Bartoli was undeterred, however, as she fired off two quick games to end the match and secure her progression.
"I was feeling quite comfortable when I was up 6-3 4-0, but she played some really good points to come back," Bartoli said.
"It wasn't a huge turning point though - I stayed focused and consistent and that's why I was able to get through that. It was a good win, straight sets and neither set going too deep."
Bartoli will next take on Sloane Stephens of the USA after she beat Tamira Paszek of Austria 6-3 6-1.
Eighth seed Lucie Safarova also made it through as Varvara Lepchenko of the USA retired with a left wrist injury, trailing 6-3 4-1. Safarova will face either Zheng Jie of China or Bulgaria’s Tsvetana Pironkova in the second round.