The 32-year-old Gasquet was 3-0 down in the opening set but rallied to win 6-4, 7-6 (3) on Monday. Another Frenchman was safely through after Adrian Mannarino beat compatriot Ugo Humbert 6-4, 6-2. He next plays 10th-seeded Kei Nishikori of Japan.
Nicolas Mahut is out of his home tournament, however, after losing to Frances Tiafoe of the United States 7-6 (1), 6-2. The 20-year-old Tiafoe will face fourth-seeded Alex Zverev of Germany. Novak Djokovic, who is aiming to wrestle back the No. 1 ranking from Rafael Nadal, will be relieved to be facing Joao Sousa of Portugal in the second round and not Marco Cecchinato of Italy.
Cecchinato, who upset Djokovic in the French Open quarterfinals, lost to Sousa 7-5, 6-3. Philipp Kohlschreiber of Germany will play fifth-seeded Marin Cilic in the next round after recovering to beat Robin Haase 6-7 (4), 6-4, 6-2.
Steve Johnson's miserable run against Roberto Bautista Agut of Spain continued. Bautista Agut improved to 6-0 against Johnson after winning 6-4, 7-6 (2) on Monday to set up a second-round meeting against ninth-seeded Grigor Dimitrov.
Elsewhere, Karen Khachanov beat last year's runner-up, Filip Krajinovic, 7-5, 6-2, and Damir Dzumhur and Feliciano Lopez also advanced. Nikoloz Basilashvili won when opponent John Millman retired with a back injury after losing their first set 6-4.
More AP tennis: https://apnews.com/tag/apf-Tennis and https://twitter.com/AP_Sports