Earlier, Simon recovered from a second-set lapse to beat Slovakian sixth seed Martin Klizan 6-4 6-4 in Metz.
Simon broke decisively in the ninth game and followed up on serve to claim the opening set.
The second-seeded Simon, however, fell 3-1 behind in the second set but he quickly regained his composure to win five of the six remaining games.
Third seed Tsonga enjoyed a 74 percent first serve rate against fifth seed Kohlschreiber, who did not have a single break chance.
Tsonga converted his only break opportunity in the first set and he continued to pile on the pressure in the second, wrapping up victory on his first match point having served a total of 13 aces.
(Reporting by Julien Pretot, editing by Pritha Sarkar)
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