It was Sochaux who made the brighter start of the two sides, with Cedric Bakambu, Ryad Boudebouz and Roy Contout testing Agassa Kossi in the early minutes of the clash.
Reims gradually grooved their way into the game, as Nicolas Fauvergue came close to breaking the deadlock in the 34th minute with a close-range header.
A minute later the home side were awarded a penalty when Sebastien Corchia handled the ball inside his own area and Corchia was subsequently sent off.
However, Kamel Ghilas failed to convert the spot kick as Pierrick Cros made the save.
Reims went close on a number of occasions in the second half as they began to take advantage of their numerical superiority.
Despite their attempts on the Sochaux goal, it was left to Sloan Privat to put the ball into the back of his own net in the fourth minute of injury time for Reims to bag maximum points.