After a 72-minute match, the scores were 6-3, 6-1.
The victory gave Gasquet his third title of the year. He earned a winner's check of $120,000.
"I am very happy to win such a prestigious tournament here in France," Gasquet said. "It is my first title in my home country and it means a lot."
The 20-year-old Gasquet ran his record to 26-8 since mid-June.
He is the youngest player this year to win three ATP titles.
Gicquel, 29, was playing in the first final of his career.