Home favourite Caroline Garcia became the highest-ranked women's player to exit the French Open so far with a second-round loss to Anna Blinkova.
Fifth seed Garcia saved eight match points before succumbing to a 4-6 6-3 7-5 defeat by the Russian.
It came after former champion Jelena Ostapenko suffered a shock defeat by tournament debutant Peyton Stearns.
But second seed Aryna Sabalenka avoided a scare with a straight-set win over qualifier Iryna Shymanovich.
Australian Open champion Sabalenka beat fellow Belarusian Shymanovich 7-5 6-2 and will face either Poland's Magdalena Frech or Russian Kamilla Rakhimova next.
Garcia was the 16th seed to exit the women's draw as the second round got under way on Wednesday.
Latvian 17th seed Ostapenko, the 2017 champion at Roland Garros, lost 6-3 1-6 6-2 to the American.
Stearns, 21, is playing in her first overseas Grand Slam after making her major debut at last year's US Open.
Her first-round victory over doubles world number one Katerina Siniakova was her first at a Grand Slam.
She will face ninth seed Daria Kasatkina next, after the Russian breezed past Marketa Vondrousova 6-3 6-4.
Third seed Jessica Pegula advanced as Italy's Camila Giorgi withdrew through injury after losing the first set 6-2.
American Pegula will next play Belgian 28th seed Elise Mertens, who defeated Colombia's Camila Osorio 6-3 7-6 (7-3).
Pegula's compatriot Sloane Stephens will face Kazakhstan's Yulia Putintseva in the third round after easing past Russian Varvara Gracheva 6-2 6-1.
Earlier, Ukraine's Elina Svitolina recovered from a shaky start to beat Australian Storm Hunter 2-6 6-3 6-1.
Three-time French Open quarter-finalist Svitolina, making her Grand Slam return after becoming a mother in October, will play Blinkova next.
Svitolina said watching her husband, French player Gael Monfils, battle to a five-set victory on Tuesday in a match which finished after midnight local time had spurred her on against Hunter.
"I was up until midnight when the match was done and went to bed straight away," she said.
"He was there for me today. He made such a big effort to come and support me, especially on a tough day like today.
"It really motivated me to fight and not give up and play every point, try to put 100% effort out there."