Vasseur completed the 143.5-mile run from Tallard to Marseille in 5 hours, 20 minutes and 24 seconds. He had to survive a five-man sprint to the finish, inching out Sandy Casar for his second career Tour de France stage victory. His other win was in 1997.
Michael Albasini was third in the stage, followed by Patrice Halgand and Jen Voigt. All five were given the same time for the stage.
Rasmussen crossed 10 minutes, 36 seconds after the leader but was in a pack that included most of the overall leaders. Because of that, he kept his overall lead at 2:35 over Alejandro Valverde, with Iban Mayo 2:39 behind Rasmussen and Cadel Evans 2:41 back.
Stage 11 of the 20-stage Tour de France is scheduled for Thursday, when riders will be covering 114 miles from Marseille to Montpellier. The tour wraps up July 29 in Paris.