Monfils took his fifth career title and second in Montpelier with a 6-4, 6-4 victory over the top-seeded and defending champion Gasquet.
Monfils won the 2010 event and finished second to Tomas Berdych in 2012. He broke a five-match losing streak in finals, improving to 5-16 all-time. His previous win came in Stockholm three years ago.
Gasquet fell short in his bid for an 11th career championship.