Last year’s runner-up Marketa Vondrousova is out of the 2020 French Open after losing 6-1 6-2 to Poland’s Iga Swiatek in the first round.
Czech Vondrousova, 21, lost to the 19-year-old, ranked 54th in the world, in a match that lasted only 63 minutes.
Svetlana Kuznetsova, the 28th seed, lost 1-6 6-1 1-6 against fellow Russian Anastasia Pavlyuchenkova.
But there were wins for third seed Elina Svitolina, fifth seed Kiki Bertens and seventh seed Petra Kvitova.
Kvitova, 30, a semi-finalist in 2012, beat France’s Oceane Dodin 6-3 7-5 after breaking her serve in the eighth game of the first set and the 11th game of the second.
A maximum of 1,000 fans were allowed into the stadium, but they did not witness a home victory as 23-year-old Dodin, ranked 117th in the world, was unable to cause an upset.
Meanwhile, Bertens recovered from a poor start against Ukrainian French Open debutant Katarina Zavatska to win 2-6 6-2 6-0.
Dutchwoman Bertens, another former semi-finalist, will play 2012 runner-up Sara Errani in the next round after the Italian qualifier beat Olympic champion Monica Puig of Puerto Rico 6-2 6-1.
Ukrainian Svitolina is hoping to make the first Grand Slam final of her career and she made a winning start with a 7-6 (7-2) 6-4 triumph against Varvara Gracheva of Russia.
Unseeded American Christina McHale moved into the second round thanks to a 6-2 6-4 success over Karolina Muchova, the 22nd seed from the Czech Republic.