Defending champion and top seed Tsonga made short work of American Jesse Levine 6-3 6-4 in straight sets, though Monfils required two and a half hours to get past second-seeded Philipp Kohlschreiber of Germany 6-7(3), 6-4, 6-4.
Monfils, seeded 10th, produced a strong comeback after dropping the first set to the man he defeated in the final of the same tournament three years ago. The acrobatic player has only just returned to the tour after a knee injury sidelined him since May.
Up next for the home hope is fifth seed Andreas Seppi of Italy, who despatched fourth-seeded German Florian Mayer 7-5 6-2.
Tsonga was broken only once and smashed seven aces en route to victory over the Canadian-born Levine, and will next face Nikolay Davydenko for a place in the 2012 final.
Eighth seed Davydenko downed Ivo Karlovic, the sixth seed, 7(5) 7-6(6) 6-0 in the late match after romping through the final set.
Davydenko had to weather a barrage of 13 aces from the big-serving Croat but raced to victory in the third set breaking three times without dropping his own serve.
Tsonga and Davydenko have met twice before, with Davydenko winning both previous matches.
The Russian, who learnt this week that he will lead his country against Great Britain in the Davis Cup, is currently ranked 48 in the world, having once been as high as three.