Top seed Caroline Garcia began her Engie Open de Limoges title defence by beating Rebecca Sramkova 6-2 7-5.
World number 24 Garcia won her two singles rubbers in France's Fed Cup final defeat to Czech Republic at the weekend and maintained that form to set up a second-round match against Lucie Hradecka, who defeated Isabella Shinikova 6-3 4-6 6-0.
Second seed Alize Cornet was taken to a third set but avoided a shock exit by downing 403rd-ranked Uzbek Akgul Amanmuradova 6-2 6-7 (5-7) 7-6 (7-3), while Garcia's Fed Cup team-mate Pauline Parmentier overcame Cindy Burger 6-0 6-2.
However, Oceane Dodin, seeded third, was unable to escape a surprise defeat as she lost 7-5 6-3 to Natalia Vikhlyantseva in the second round.
At the OEC Taipei WTA Challenger, Russian sixth seed Evgeniya Rodina advanced to the quarter-finals by coming from behind to eliminate Dalila Jakupovic 2-6 6-4 6-1.
Olga Govortsova's strong run continued as she defeated Julia Boserup 5-7 7-6 (7-5) 7-5 to set up a clash with wildcard Vitalia Diatchenko in the last eight.