The fifth-seeded Berdych, who won the Paris event in 2005, moved on with a quick 7-6 (8-6), 6-2 win over Andreas Seppi.
Sixth-seeded 2008 titlist Tsonga, meanwhile, battled past fellow Frenchman Julien Benneteau 6-2, 4-6, 7-6 (7-2) to also reach the second round in Day 2 action.
Breaking through to the third round Tuesday were Poland's Jerzy Janowicz, who bested 13th- seeded Croat Marin Cilic 7-6 (8-6), 6-2, and 15th-seeded Japanese Kei Nishikori, who logged a 7-6 (7-2), 6-2 win over France's Benoit Paire.
No. 16 Stanislas Wawrinka of Switzerland also posted a 6-3, 6-2 second-round decision over Argentine Carlos Berlocq.
Other first-round winners Tuesday included American Sam Querrey, France's Paul-Henri Mathieu, Bulgarian Grigor Dimitrov, Dutchman Igor Sijsling, Frenchman Michael Llodra and France's Jeremy Chardy.
Celebrity Families of 2014 [PHOTOS]