Stephens won in straight sets but it took almost two hours, triumphing 7-5 6-4 over the Frenchwoman ranked just outside the top 100.
The 28-year-old American was dominant on her first serve, while she broke her opponent five times throughout the match.
Stephens, who is the No.6 seed, will play Daria Saville in the last eight after the Australian eased past qualifier Caroline Dolehide 6-1 6-3 in one hour and seven minutes.
No.3 seed and defending champion Sara Sorribes Tormo made light work of Poland's Magdalena Frech 6-0 6-2 to set up a quarter-final meeting with Marie .
Colombian Camila Osorio, the No.4 seed, needed just over two hours to get past Hailey Baptiste 1-6 6-3 6-3, fighting back after a lopsided first set.