World No. 98 Ferro overcame defending champion Cornet 6-1, 2-6, 6-1 in one hour and 40 minutes.
It was the first all-French WTA final in 10 years and Ferro clinched the title with her seventh break of serve from nine chances when Cornet sent a forehand long.
"I'm very happy and very relieved," Ferro told the reporters after the final. "It was a very tough match against a fellow French player and a friend -- it was very difficult to stay calm and to stay in the moment.
"When you play a friend the emotions always take over."
Both players represent the club in Nice and Cornet described her fellow countrywoman as "like my little sister on the tour."
Ferro managed to secure victory without her coach Stéphane Huet who was on holiday at the time of the final.
"It's funny -- he made jokes about it and told me he would get fired," said Ferro. "But I hope we can win a title together now."
Ferro was playing her first final on tour, while Cornet dropped to a career record of 6-7 in title matches.
Information from The Associated Press was used in this report.