The 42nd-ranked Cornet was too strong and consistent for the misfiring Canadian, winning the decider in 68 minutes in windy conditions.
But as much as seventh seed Cornet dominated, former world number five Bouchard was well off her game, losing serve seven times, producing five double faults and serving at just 48 percent.
Cornet broke Bouchard’s opening service game and then gave back the service break before reeling off five straight to take the first set.
Bouchard broke Cornet’s opening service in the second set and led 2-0 before the French star won six games in a row to take the set and the match.
It was 25-year-old Cornet’s first WTA title since winning at Katowice in 2014, and gave her a perfect tune-up for next week’s Australian Open in Melbourne.
Cornet will face Serbia’s Bojana Jovanovski in the first round of the year’s opening Grand Slam, with a possible second-round clash with second seed Simona Halep.
The 47th-ranked Bouchard, who beat three seeded players — Alison Van Uytvanck, Camila Giorgi and Dominika Cibulkova — on the way to the Hobart final, takes on another Serb Aleksandra Krunic in her first-round match in Melbourne.