Paris Ashleigh Barty is knocking on the door of the world's top five after booking a career-best third round showing at the French Open.

Entering the slam at a high of No.8 in the world, even a loss to Danielle Collins would've seen her jump provisionally to sixth before the Wimbledon tournament starts in July.

Barty can climb higher than that though, with a gritty 7-5 6-1 win on a damp, cold Paris afternoon continuing the Australian's charmed 2019 run.

Meanwhile, Australia veteran Samantha Stosur looks set to drop out of the world's top 100 after her remarkable decade-long French Open run was halted by powerful Russian Ekaterina Alexandrova in the second round.

Stosur had made at least the third round in her last 10 visits to Roland Garros, a streak only matched on the Paris clay among active players by Maria Sharapova.

She looked set to extend that after racing to a one-set lead before the world No.58's booming groundstrokes found their range in a gutsy 3-6 6-1 6-4 win.

AAP