The 98th-ranked Ferro plays for the same club in Nice as No. 48 Cornet, who described her as "like my little sister on the tour."
Ferro clinched the title with her seventh break of serve from nine chances when Cornet sent a forehand long.
Third-seeded Cornet was the defending champion, though the clay-court event was played last year in the ski resort of Gstaad.
The 22-year-old Ferro was playing her first final on tour, while Cornet dropped to a career record of 6-7 in title matches.