Australia's Kyrgios had breezed into the last four without dropping his serve but faced an opponent in decent form, with Tsonga having taken last week's ABN Amro World Tennis Tournament title in Rotterdam.
The volatile Australian was unable to defend his Marseille crown as he lost to Jo-Wilfried Tsonga 7-6, 2-6, 6-4 on Saturday, 25 February.
Victory yesterday in the final would mean a career first for Tsonga of back-to-back ATP Tour triumphs and marks a real return to form for last year's US Open quarter-finalist.
Tsonga never faced a break point as he added a third Marseille title to his collection after victories in 2009 and 2013.
Kyrgios, the third seed, was beaten 7-6 (7-5), 2-6, 6-4 by the second-seeded Frenchman Tsonga, who will meet countryman Lucas Pouille in the finals.
"I've seen referees wait 5-6 seconds after the ball's gone out", Kyrgios said.
Tsonga hit seven aces, dropped only three points on his first serve and did not face a single break point.
The 23-year-old Pouille won the opening set by breaking Gasquet in the 12th game and carried the momentum into the second set by winning the first five games to remove any suspense. I will have to make choices', said Tsonga after the title won in Marseille. I served very well when I needed too and for Lucas it was hard to create opportunities.'â.