The incident took place as Barthez was leaving Beaujoire Stadium Saturday night after a 2-0 loss to Rennes all but doomed the Canaries to relegation after 44 consecutive years in the top flight.
Nantes president Rudi Roussillon said five drunken fans kicked Barthez's car and banged on the windscreen, and one fan tried to open the car door. Barthez got out and trade punches with one of the fans before they were separated by security guards.
Barthez had joined Nantes in January after being out of work following the 2006 World Cup in which he started for runner-up France. But the 35-year-old keeper's play has been poor, making him an easy target for fans unhappy with the Canaries' decline.
Roussillon said Barthez left town with his children and might not return.