The top-seeded defending champion Gasquet battled past No. 3 seed Jerzy Janowicz of Poland 7-6 (8-6), 7-6 (7-4) to claim his berth in the all-French finals.
Gasquet -- has not lost a set this week -- weathered 16 aces from Janowicz and won 80 percent of his first-service points.
Monfils, who is seeded fifth, upended sixth-seeded Jarkko Nieminen of Finland 6-2, 3-6, 6-1.
Monfils won the tournament in 2010 and has a 5-4 career record against Gasquet.
Teacher apologizes for showing sexual image of herself in class
Senate Democrats to pull all-nighter on climate change