The seventh-seeded Cornet, ranked 73rd, earned her second career title after winning in Budapest, Hungary, in 2008. She is 2-3 in WTA finals. She lost the final in Strasbourg last month.
"This was the tournament I wanted to win this year," Cornet said. "I can't believe I didn't win a title for the last four years so now it's all happiness."
Cornet broke the second-seeded Wickmayer's serve at 5-5 and then held to take the opening set.
She was 5-3 up in the second set against Wickmayer, and then dominated the tiebreaker.
Cornet converted her first match point as Wickmayer sent a forehand into the net.