In the first semifinal, Pouille rallied to beat Kyle Edmund of Britain 6-7 (7), 6-4, 6-4 to reach his fourth final of the season. He won titles in Budapest and Stuttgart.
The 15th-ranked Tsonga, who won the event in 2011, is after his fifth title of the year.
He has not dropped a set against Pouille in their two previous meetings.
A day after defeating top-seeded Alexander Zverev in the quarterfinals, Tsonga improved to 11-1 against Kohlschreiber. The Frenchman recovered from a break down to win the opening set, and added another break at 5-5 in the second.