Monfils, the No. 3 seed, dispatched American Michael Russell 6-3, 6-3. The world No. 13 fired 17 aces and won 84 percent of his first serves.
The top four seeds, including Berdych and Monfils, had received byes into the second round on the indoor hardcourts at the Arena Montpellier.
Berdych, coming off an Australian Open performance that saw him reach his fifth career Grand Slam quarter-final, will take on big-serving Nicolas Mauht in Friday's quarterfinals. Mauht edged sixth-seeded German Florian Mayer 7-6 (7-3), 6-3 on Thursday.
Monfils, winner of this ATP World Tour 250 event when it was last contested in 2010, will face eighth-seeded Jarkko Nieminen of Finland on Friday. Nieminen defeated French wild card Paul-Henri Mathieu 7-6 (7-4), 6-1 on Thursday.
The remaining quarterfinal matches on Friday feature second-seeded Gilles Simon against fellow Frenchman and wild card Guillaume Rufin, and fourth- seeded slugger Richard Gasquet taking on seventh-seeded Philipp Kohlschreiber.
The winner of this $518,000 tournament will collect $95,000.