The 2008 winner came into his match against Japanese opponent Kei Nishikori as an overwhelming favourite but ended up on the wrong end of a 1-6 7-6 (7/4) 7-6 (9-7) scoreline.
Tsonga was in complete control in the first set and sent down six aces as he raced ahead but Nishikori upped his first service to 64 per cent as he evened things up in the second.
The deciding set was even tighter with neither man being able to break the other and it was the world number 19 who won the tie break to move into round three.
There was more disappointment for the home crowd but it was somewhat more expected as second seed Novak Djokovic beat French qualifier Pierre-Hugues Herbert.
Herbert put up a real fight in the first set but he could not find a break and, despite fighting back from 5-0 down in the second, he succumbed to a 7-6 (7/3) 6-3 defeat.
Ninth seed Richard Gasquet was a home hope who did advance to the third round as he claimed a tight win over Fernando Verdasco.
A single break of serve was enough to hand Gasquet the first set but his Spanish opponent fought back to take the second set on a tie break.
Gasquet was not to be denied, though, and Verdasco was broken twice in the third as the world number 10 won 7-5 6-7 (6/8) 6-3.
Nicolas Mahut advanced to the second round thanks to a 7-6 (8/6) 6-1 win over Alexandr Dolgopolov but it was an otherwise poor day for the unseeded home competitors.
Michael Llodra took the first set against Grigor Dimitrov but could not seal the win as the world number 22 emerged a 6-7 (5/7) 6-3 6-3 winner.
Edouard Roger-Vasselin was also beaten by a higher-ranked opponent as he went down 7-6 (8/6) 6-4 to Ivan Dodig.
In the afternoon's other matches, Pablo Andujar defeated Vasek Pospisil 6-4 2-6 6-4, Michal Przysiezny saw off Jarkko Nieminen 6-3 7-6 (8/6) and Marcel Granollers was a 6-4 6-4 victor over Dmitry Tursunov.
Kevin Anderson beat Mikhail Youzhny in an evening clash as the Russian retired with the scores at 4-6 7-6 (7/0) 2-1 while last year's beaten finalist Jerzy Janowicz beat qualifier Santiago Giraldo 7-6 (7/3) 6-3 in the second round.