Cornet won her fifth WTA title and first since April 2014 in her third attempt at the Hobart International, one of the Australian Open Series warm-up tournaments.
Bouchard gave her best performance since a lengthy layoff caused by a concussion she suffered in a dressing room fall at last year's U.S. Open.
On Saturday, Bouchard had some difficulty in the breezy conditions, serving five double faults.
"It was a tough one for me," she said. "I just wasn't on top of my game."