Paris - Top seed and 2016 champion Novak Djokovic continues his bid to hold all four Slams at once for the second time on Thursday.
Naomi Osaka, who was just two points from defeat in her opener, faces another minefield in the shape of former world number one and two-time major winner Victoria Azarenka.
Three-time winner Serena Williams, who is looking for a record-equalling 24th major, faces Japanese qualifier Kurumi Nara.
A look at the three matches to watch:Naomi Osaka (JPN x1) v Victoria Azarenka (BLR)
- US and Australian Open champion Osaka was just two points away from a shock defeat in the first round to world number 90 Anna Karolina Schmiedlova who twice served for the match.
"I think this was the most nervous I have ever been my entire life during a match," said 21-year-old Osaka.
Azarenka, now ranked 43, knocked out 2017 champion Jelena Ostapenko in the first round and was a semi-finalist in Paris six years ago.
She came into Paris with solid clay court form having made the quarter-finals in Stuttgart and Rome.
Azarenka won her first match against Osaka at the Australian Open back in 2016 but the Japanese star levelled their head-to-head, dropping just three games in a second round win on clay in Rome last year.Novak Djokovic (SRB x1) v Henri Laaksonen (SUI)
Head-to-head: First meeting
- Djokovic eased through his opener in straight sets against Poland's Hubert Hurkacz as he bids to become only the second man to hold all four Slams simultaneously for a second time.
The top seed faces Swiss lucky loser Laaksonen who has made the second round of a major for the first time.
The Finland-born world number 104 recently conquered a debilitating allergy to seafood despite having eaten fish virtually every day for all of his adult life.
"I don't know too much about him, to be honest," said Djokovic.
"I never played against him, and I did watch him play maybe once or twice. I'm going to have to do my homework and see what happens."Serena Williams (USA x10) v Kurumi Nara (JPN)
Head-to-head: First meeting
- Three-time champion Williams looked rusty in her opener against Vitalia Diatchenko where she dropped the first set.
The American, who is attempting to equal Margaret Court's all-time record of 24 Grand Slam titles, racked up her 800th career main draw win in a match which saw her unveil her 'mother, champion, queen, goddess' logo on her playing gear.
On Thursday, she faces world number 238 Kurumi Nara who stands just 5ft 1in (1.75m) tall but can mix it with the best of them.
In the 2017 US Open, she ruthlessly demolished 2004 champion Svetlana Kuznetsova.
The 27-year-old Nara, a former world 32, came through qualifying and is bidding to make the third round for the first time.