The 2008 champion was forced into a final-set tiebreaker after failing to serve out the match.
Benneteau only converted three of his 11 break-point chances against the hard-serving Tsonga, who hit a total of 15 aces -- five in each set.
Novak Djokovic is among the favorites for the tournament, which is missing Roger Federer and Rafael Nadal. Djokovic, who has clinched the year-end No. 1 ranking, will face Sam Querrey of the United States on Wednesday.
"It's obviously really satisfying and I'm delighted," Djokovic said of finishing No. 1 for a second year in a row. "This shows how good my season has been. I'm proud of what I've done because it wasn't easy to repeat after the incredible season I had in 2011. But it's not over, Paris and London next week are two very important tournaments and I want to try and focus on them."
Djokovic said he came into the 2012 season conscious of his schedule and trying to avoid the same kind of injuries which forced him out of tournaments late last year.
"Aside from the Olympic Games, the scheduling has been terrific for me," he said. "I haven't played that many tournaments and I've tried to focus to always perform my best at the major events."
In other second-round matches, fifth-seeded Tomas Berdych of the Czech Republic beat Andreas Seppi 7-6 (8), 6-2, No. 13 Marin Cilic lost to qualifier Jerzy Janowicz of Poland 7-6 (6), 6-2, No. 15 Kei Nishikori of Japan had a 7-6 (2), 6-2 win over Frenchman Benoit Paire and No. 16 Stanislas Wawrinka of Switzerland defeated Carlos Berlocq of Argentina 6-3, 6-2.
After a close first set, Berdych took control of the match by jumping out to a 4-0 lead in the second.
Janowicz pulled off his second upset win of the tournament when he beat Cilic in straight sets to move into a potential third-round match against U.S. Open champion Andy Murray.
Janowicz, who ousted 19th-seeded Philipp Kohlschreiber in the first round, did even better against the big-serving Croat and never faced a break point.
It was the 21-year-old Janowicz's first victory against a top-15 player.
In first-round matches, three Frenchmen advanced with wins against Spaniards. Jeremy Chardy cruised past Guillermo Garcia Lopez 6-0, 6-3, Paul-Henri Mathieu beat Roberto Bautista-Agut 6-4, 7-5, and Michael Llodra defeated Daniel Gimeno-Traver 7-5, 6-3.
In other first-round action, Grigor Dimitrov beat Jurgen Melzer 7-6 (2), 6-2 and Igor Sijsling defeated Alexandr Dolgopolov 6-4, 6-2, while Sam Querrey of the United States advanced after Fernando Verdasco retired when trailing 6-1, 1-1.