The current world No.8 beat American Danielle Collins 7-5 6-1 on a damp, cold Paris afternoon.

Even if Barty were to suffer a loss, she was projected to jump to sixth ahead of Wimbledon in July.

The 23-year-old saw off the Australian Open semifinalist in a see-sawing first set, which saw Collins break Barty twice before executing a clinical finish.

Barty will play German Andrea Petkovic on June 1 and the Queensland could meet three-time Roland Garros champion Serena Williams in the fourth round.

Fellow Australian Sam Stosur wasn't as lucky in the singles with her decade-long French Open run halted by Ekaterina Alexandrova who took a 3-6 6-1 6-4 win.

The 35-year-old has made at least the third round in her last 10 visits to Paris.

However, in the doubles, Stosur continued her fine form with partner Zhang Shuai for a straight sets win over Veronika Kudermetova and Galina Voskoboeva. 

The pair only dropped three games on their way to making the second round. 

Meanwhile, Priscilla Hon played in one of the final women's singles matches of Thursday and she pushed world No.14 Madison Keys throughout. 

It was only in the 13th game of the first set that the American was able to break to win but Hon would force a third set by taking the second. 

But the play was suspended just as the third set go underway due to poor lighting.