Barthez was apparently insulted by an angry Nantes fan as he was driving out of the Beaujoire stadium. The former world and European champion got out of his car and the two men started trading punches. Security staff moved in to separate them.
Neither Barthez nor the club were available for comment.
Eight-times champions Nantes are on the verge of being relegated for the first time.
Nantes, who have spent a record 44 consecutive years in the top flight since being promoted in 1963, are now eight points from safety at the foot of the table with four matches left.
Barthez came out of retirement in mid-December to help Nantes in their bid to escape relegation. The bald-headed 35-year-old has, however, committed some embarrassing blunders reminiscent of his worst days at Manchester United.
He has also stirred controversy, most notably after conceding a clumsy goal in a 1-0 defeat at home to lowly Sedan earlier this month. After being substituted with an injury, he left the stadium straight away without even waiting for the end of the game.
