Fourth-seeded Aleksandra Wozniak injured her right shoulder during the warmup session and was unable to start the match.
Wozniak's retirement left only one of the tournament's first five seeds still in action heading into Friday's quarterfinals.
Oudin, seeking her first championship on the WTA Tour, will meet qualifier Kristina Mladenovic in the quarterfinals. Mladenovic advanced Wednesday with a second-round win over Annika Beck.
Another of the quarterfinals will bring together players who have never come close to winning on the tour.
Kirsten Flipkens ousted Mirjana Lucic in the second round Thursday 6-7 (2-7), 6-4, 6-4, and will take on Anna Tatishvili. Flipkens eliminated top-seeded Dominika Cibulkova in the second round.
Tatishvili defeated seventh-seeded Petra Martic 6-2, 6-3 on Thursday.
In the only other second-round match played Thursday, Lucie Hradecka outlasted Eugenie Bouchard 7-6 (7-2), 2-6, 7-6 (7-4). Hradecka's quarterfinal opponent will be Lauren Davis, who eliminated second-seeded Yanina Wickmayer Wednesday.
The top seed remaining in the event is No. 3 Mona Barthel, who will face sixth-seeded Barbora Zahlavova Strycova Friday.