It was the perfect Roland Garros warm-up for the Italian who has made the last two French Open finals - winning the title in 2010 and finishing runner-up to Li Na in 2011.
She had won just two matches on clay in seven tournaments in 2012 prior to this week but claimed the title in 104 minutes after breaking her unseeded opponent on five occasions during the match.
Home favourite Cornet, in her first WTA final since 2008, did break Schiavone on three occasions but was hampered by a thigh injury she suffered early in the second set.
It was 32-year-old Schiavone's first title since winning in Paris two years ago. She faces Kimiko Date-Krumm in her opening match on the French clay.