The unseeded Vandeweghe served 11 aces and broke her French opponent's serve eight times in a 4-6, 6-3, 6-1 victory.
Germany's Kerber had an easier time dispatching American Samantha Crawford 6-3, 6-3.
Third-seeded Maria Kirilenko of Russia advanced with a 7-5, 6-1 win over Mexico's Ximena Hermosa. Fourth-seeded Ana Ivanovic of Serbia sent Russian Marta Sirotkina packing in 45 minutes by a score of 6-0, 6-0.
Notable deaths of 2014 [PHOTOS]
Michael Sam cut from the Dallas Cowboys