Isner had 10 aces and broke his opponent three times to wrap up the match in 67 minutes.
Isner won a historic first-round match at Wimbledon earlier this year that went a total of 183 games and 11 hours, 5 minutes. He will next face another Frenchman, qualifier Adrian Mannarino.
Mannarino had 15 aces and needed eight match points to beat Slovakian Lukas Lacko 6-3, 6-7 (4), 6-4.
Taylor Dent, another big server from the United States, rallied from one set down to beat Romain Jouan of France 6-7 (5), 6-3, 6-4.
Dent lost six consecutive points in the first-set tiebreak but recovered to wrap up the match in 1 hour, 58 minutes after having 20 aces and saving the six break points he faced.
Dent will play fourth-seeded Ivan Ljubicic of Croatia in the second round.
Zverev will next face top seed Nikolay Davydenko of Russia.