It wasn't smooth sailing for Australia's top-ranked star as Barty beat American Jessica Pegula 6-3 6-3 while Stosur secured a 6-2 7-6 win in a second-set tiebreak.

While Barty led 4-0 in the first set, her American opposition broke back twice and forced the 23-year-old Australian to break again before securing the set.

It was an uncharacteristic game from Barty, who is the world No.8, as she let leads slip during sets to give Pegula a small taste of an upset win. However, it wasn't meant to be the American as she claimed her 25th win of the season in an hour.

Barty will be hoping to continue her form against Australian Open semi-finalist Danielle Collin on Wednesday. Barty has never progressed beyond the second round at the French Open.

The win takes her to 25-5 this season, having skipped last week’s Strasbourg International to manage an arm injury she says should not impact her performance in Paris.

For Stosur, she continued her consistent performance on clay as she looks to continue her decade long run of making the third round.

The former world No.1 will face Russian Ekaterina Alexandrova. 

However, fellow Australian Astra Sharma was knocked out by American Shelby Rogers 6-3 6-3.

On Tuesday, Alja Tomljanović, Daria Gavrilova and Priscilla Hon will take to the clay court for their first round matches.