Federer -- a one-time champion at Roland-Garros -- easily dispatched of German counterpart Oscar Otte 6-4, 6-3, 6-4. The match lasted one hour, 36 minutes. The 20-time Grand Slam champion has a third-round matchup against Casper Ruud on Friday in Paris.
Bertens lasted 21 minutes in her second round clash with Viktoria Kuzmova, before dropping out. She trailed 3-1 in the first set against her Slovakian opponent prior to her decision to exit the tournament.
The No. 4 player in the world was among the favorites to win the women's circuit. Bertens told reporters she felt good on Tuesday while practicing and resting. She woke up at 3 a.m. on Wednesday with stomach sickness. Bertens experienced discomfort again while she was warming up.
"It's really bad timing, I would call it maybe that," Bertens said. "It's been a great few weeks, and then if you feel like this during a Grand Slam where you felt good, it's just really annoying."
"I just hope I feel better soon but probably that won't be the case."
Bertens beat Pauline Parmentier in straight sets Monday in her round of 128 match. She has never reached a Grand Slam singles final. Bertens advanced to the French Open semifinals in 2016 and went to the quarterfinals in 2018 at Wimbledon.
No. 2 Karolina Pliskova, No. 9 Elina Svitolina and No. 7 Sloane Stephens were among those who advanced into the third round on Wednesday in the women's circuit. No. 2 Rafael Nadal, No. 6 Stefanos Tsitsipas, No. 7 Kei Nishikori joined Federer among the top men's players to advance to the round of 32 with wins on Wednesday.