Schiavone, winner of the French Open in 2010, eliminated Johanna Larsson 6-0, 6-3 to move closer to what would be her first title of the year.
Her semifinal opponent will be Sloan Stephens, who defeated Ayumi Morita 6-3, 6-4.
The French Open begins Monday in Paris, where Schiavone finished as the runner-up last year in defense of her championship.
Cornet surprised fourth-seeded Medina Garrigues 7-6 (7-2), 7-6 (7-5) while Cornet defeated Alexandra Panova 6-3, 6-3.
2014: NFL Cheerleaders [PHOTOS]
Michael Sam cut from the Dallas Cowboys