Tsonga has won 10 career titles but only one this year at the Open 13 in Marseille in February. This is Tsonga's first tournament since a knee injury forced him to drop out of his second-round match at Wimbledon.
The 80th-ranked Kamke has never won an ATP tournament and it was only his second quarterfinal of the season. He saved eight break points in the first set and converted his first against Tsonga to move ahead.
Tsonga then broke Kamke once in the second and third sets and next faces eighth-seeded Florian Mayer of Germany, who rallied to beat Argentina's Carlos Berlocq 5-7, 6-4, 7-5 to reach his second semi this season.
Simon took control of the tiebreaker by hitting a forehand passer down the line to open up a 3-1 lead.
He then forced an error at the net from Querrey, who swiped his racket in frustration after losing the next point. Simon hit a crisp forehand winner that set up five match points and he converted the first when Querrey's awkward shot sank into the net.
The 31-year-old Mahut is blossoming late in his career and won his first two singles titles this summer.
Simon, the 2010 champion, is chasing his first title of the season after reaching his fifth semifinal of the year.