The African nation of Rwanda issued the warrant in November and Musabyimana was arrested Tuesday in Dijon, Radio France International reported Thursday.
French officials say they do not know anything about him or how long he has been in the country. He was driving a delivery van when arrested, authorities said.
A group dedicated to finding genocide suspects in France also said they knew nothing about him.
Prosecutors in Rwanda say they have requested his extradition on charges of genocide, murders and rape during a 1994 conflict.
A judge in Dijon says he will rule on the request by Jan. 30.