The American, a three-time winner at Roland Garros, fell 3-0 down in a first-set tie-break in a match dominated by powerful serves before recovering to prevail 7-4.

She then clinched the second set 6-4 to set up a second-round tie with Ashleigh Barty of Australia.

The 23-time Grand Slam singles champion was competing in her first Grand Slam match since she returned to tennis in March following six months out to give birth to her first child.

It was also her first match on clay since 2016. 

"Kristyna played really, really well," Williams said.

"I don't know how many aces I saw during the match, I think there is a donation to charity for each ace, so both of us helped.

"Two years is a long time but I've trained hard on this surface.

"I'm so glad to win a match here and I'm taking it one day at a time."

Maria Sharapova was another former champion to reach the second round of the women's singles draw today.

The Russian, a winner in 2012 and 2014, overcame a mid-match wobble to beat Dutch opponent Richel Hogenkamp 6-1, 4-6, 6-3.

Third seed and 2016 winner Garbiñe Muguruza of Spain beat Russia's 2009 champion Svetlana Kuznetsova 7-6, 6-2 elsewhere today.

Rafael Nadal completed his first round victory over Italy's Simone Bolelli after the tie was delayed overnight.

The Spaniard, chasing an 11th French Open title, was forced to dig deep before winning a decisive tie break for a 6-4, 6-3, 7-6 success,

Argentina's Guido Pella will be his next opponent in the second round.

Third-seeded Croat Marin Čilić beat Australia's James Duckworth 6-3, 7-5, 7-6 in other matches today.