Alexis Peuget opened the scoring for Rumilly before they were overwhelmed by the Ligue 1 side, who booked their ticket for Wednesday's showdown at the Stade de France with an own goal by Arthur Bozon and goals by Aurelien Tchouameni, Wissam Ben Yedder, Cesc Fabregas and Aleksandr Golovin.
PSG qualified on Wednesday by beating Montpellier on penalties after a 2-2 draw.
Rumilly took an unexpected lead in the 20th minute when Peuget fired home after collecting Joris Cottin's back pass following a bad clearance by Djibril Sidibe.
Monaco quickly levelled, however, as Arthur Bozon turned Fode Ballo Toure's cross into his own net.
Tchouameni gave Monaco the advantage in the 32nd minute when he headed home from Fabregas's corner before Ben Yedder added a third with a delicate chip after a one-two with Fabregas 10 minutes into the second half.
Fabregas put the result beyond doubt 12 minutes from time with a curled free kick and Golovin completed the rout with a low shot.