Among the women, No. 1 Simona Halep shook off a slow start in a postponed first-round match to defeat Alison Riske of the USA 2-6, 6-1, 6-1, while second-round winners included reigning major champions Caroline Wozniacki and Sloane Stephens, along with No. 4 Elina Svitolina, No. 8 Petra Kvitova and No. 13 Madison Keys.
Halep, who will lose the world number one ranking if she fails to make the last four, suffered a scare in her opening round match, rallying from a set down to beat Alison Riske yesterday, though was much more comfortable on Court Philippe Chatrier today. Halep was dominant in the second round, winning 54 percent of her return points and producing just 13 unforced errors.
Wozniacki, who won her first Grand Slam trophy at the Australian Open this year, limited her mistakes to eight unforced errors. Nadal has since become a multiple Grand Slam victor and the most successful clay-court player ever, while Gasquet did not live up to the huge expectations surrounding him at the start of his professional career.
It came on a day of five-set tests for a trio of top players in round two of the men's draw at Roland Garros.
Williams, who made her Grand Slam return with a singles win on Tuesday, is back in action in the doubles with sister Venus later on Wednesday.
Alexander Zverev also reaches for the controller when he gets home from Roland Garros. "It was good that I came back so strong", Halep, beaten in last year's final by Jelena Ostapenko, said.
'I had a slow start because it's always tough to start this tournament.
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And Muguruza impressed with her easy movement around the court in a 6-4, 6-3 victory over French wild-card entry Fiona Ferro.
Riske, meanwhile, wilted and won only 22 points in losing the second and third sets.
In other matches among the women, second-round winners included Denmark's Caroline Wozniacki, ranked No. 2, and Sloane Stephens of the United States, ranked 10th, along with Ukrainian Elina Svitolina (No. 4), Czech Petra Kvitova (No. 8) and American Madison Keys (No. 13).
She uses its every line and angle, moving opponents around, trying to take away from their fire power like she did with American Taylor Townsend in her second-round outing on Thursday.
Nadal hasn't lost a set at the French Open since 2015, when he was beaten in the quarterfinals by Novak Djokovic. She missed the clay-court Grand Slam tournament in 2016 while serving a doping suspension, then was denied a wild-card entry by the French tennis federation a year ago, when her ranking was too low to earn automatic entry.