The indoor showpiece has former US Open victor Marin Cilic as top seed, with the 2014 finalist starting the latest edition against quirky Frenchman Benoit Paire on Tuesday.
Zverev booked his place after beating home favourite Jo-Wilfried Tsonga 6-7 (8/6) 6-2 6-4 to reach his fourth career ATP World Tour final.
Defeat ended world number 22 Gasquet's 10-match winning streak in Montpellier.
After exchanging early breaks of serve, Dimitrov, who defeated Kei Nishikori last month to win the Brisbane International, made the all-important breakthrough in game 12 on his way to the first set. I'm very happy the way we played.
The match was not without controversy, however, as Goffin complained to the chair umpire about the hostile crowd at the end of the first set.
The second set started out much as the first set did with each player trying to control proceedings from the baseline. With Gasquet trying to keep up with his younger opponent, it was Zverev who finally earned the pivotal service break. He punished Paire's poor serving, converting five of his seven break points. He squandered all three with several loose errors but gained a fourth match point thanks to an ace.
Goffin beat Bautista Agut 5-7 6-4 7-6 (7/3) and will face Grigor Dimitrov as he goes for his third career title.
Zverev hit 32 winners and 32 unforced errors compared to 17 winners and 24 unforced from Gasquet.
"It was a very successful tournament for the Zverevs", Alexander Zverev said.