Richert represented Les Lionceaux almost 300 times in a 10-year spell with the Montbeliard outfit.
He told L'Equipe: "I've decided to stop, I think I've given a lot and taken a lot too.
"But this is the right time.
"I've played for a lot of years at a high level and fatigue has set in."
Having started his career with Toulouse, Richert joined Sochaux in 2002 and was named Ligue 1 goalkeeper of the year as Sochaux won the Coupe de
French champion Paris Saint-Germain has reportedly commenced discussions with Wayne Rooney with a view to signing the want-away Manchester United striker.