Serena Williams
Pictured: Serena Williams of The United States celebrates during the ladies singles second round match against Ashleigh Barty of Australia during day five of the 2018 French Open at Roland Garros on May 31, 2018 in Paris. Clive Brunskill/Getty Images

23-time Grand Slam winner Serena Williams is hoping to go beyond the level of her pre-pregnancy days after reaching the third round of the French Open Thursday.

Donning her Wakanda-inspired catsuit again, Williams came back from a set down to defeat Australia's Ashleigh Barty 3-6, 6-3, 6-4 as she continued her quest for a joint-record 24th Grand Slam with Margaret Court currently holding the record.

Despite many unforced errors in the first set, the American feels she didn't play that bad, but, was pleased she was able to bounce back in what was a much tougher test for her.

"I felt like in the first set I didn't play bad. I just didn't make any shots," Williams said after the match, as per BBC. "So I guess it is bad. But I had all the right ideas, like coming to the net and hitting all my shots. They just weren't going in.

"For me, that was kind of like a positive thing, because it wasn't like I was playing the ultimate match. I was just making so many errors. I thought I've got to cut down on the errors, and I've just got to come out here and fight. And that's what I did."

Williams is playing in her first Grand Slam since winning the 2017 Australian Open, which, she later revealed she won while she was eight weeks pregnant.

Having taken time away from the sport for nearly 14 months soon after, the 36-year-old returned at the BNP Paribas Open in March where she won two matches before losing to her sister Venus.

She would then lose her opening round game in the Miami Open to Naomi Osaka, but, with the two wins at Roland Garros, Williams admitted she is still not at the level she was before her maternity leave. However, she is hoping to return to that level and be even better than before.

"I'm probably not where I was before I left," Williams continued. "I'm definitely going to get there, but I also want to get beyond there."

Williams will now meet Germany's Julia Goerges in the third round after the 11th seed defeated Belgium's Alison van Uytvanck of Belgium in straight sets.

Meanwhile, world No. 1 Simona Halep beat American Taylor Townsend in a straight-set 6-3, 6-1 win and will now face Germany's Andrea Petkovic.

Reigning Wimbledon champion Garbine Muguruza defeated France's Fiona Ferro 6-4, 6-3 and will meet Australia's Samantha Stosur in the third round.

"It's always tricky when you face a young, talented French player," Muguruza reflected after. "It probably wasn't the best tennis out there but I'm happy that I managed to fight and to win."

Two former No. 1s in Maria Sharapova and Karolina Pliskova will clash in the third round after respective wins over Donna Vekic and Lucie Safarova.

Last year's winner, Latvia's 20-year-old Jelena Ostapenko, notably crashed out in her first round match against Kateryna Kozlova.