The 18-year-old was in impressive form on Tuesday, hitting 11 aces and 28 winners as she wrapped up a 6-2 6-3 first-round victory over Oudin in 75 minutes.
Robson joins fellow Brit Heather Watson in round two, with the teenager set to face the 2011 Wimbledon champion on Thursday.
“I will go in with nothing to lose. I seem to do well when I do that,” said Robson.
“It’s going to be tough, two lefties playing each other. I haven’t played a lefty in a while so I will just do the best I can.”
Robson was pleased with her performance on Tuesday but recognises that an improvement is needed if the Brit is to topple eighth seed Kvitova.
“I think I played pretty well, just not as well as I would have liked to. Hopefully in the next match it will be a bit better,” said Robson.
“I can hit it pretty hard these days but I think the key is moving around the ball enough to get it to where I want it to go every time.
“Today I just hit a few balls late here and there, where I should have just moved my feet a little bit.”
MORE: The latest football news
MORE: The latest tennis news
BIOGRAPHY: Daniel Sturridge
BIOGRAPHY: Kepa Arrizabalaga