The public session was about to begin when a heated dispute started at the centre of the pitch between Evra and Duverne.
France coach Raymond Domenech had to move in to separate them. Duverne angrily threw his stopwatch on to the pitch and left.
The players then walked towards their bus following the incident, a day after striker Nicolas Anelka was sent home after insulting Domenech at half-time of a 2-0 defeat by Mexico on Thursday in Polokwane.
“They don’t want to train, it’s a scandal,” France team director and French Football Federation managing director Jean-Louis Valentin said as he also left the pitch.
“It’s a scandal for French people, for the youngsters who came here to watch them train. I’m resigning, I’m leaving the Federation. I have nothing more to do here. I’m going back to Paris.”
The new scandal came a day after Evra said a “traitor” within the team had leaked Anelka’s insults to the press.
French sports daily L’Equipe put them on their front page and a few hours later, Anelka was kicked out of the squad.
Asked by a reporter on Sunday if he was the “traitor”, Valentin replied “no, no, no” and appeared close to tears.
French media suggested on Sunday that Anelka’s attitude was not the only problem in France’s troubled squad and reported rival playmakers Yoann Gourcuff and Franck Ribery had a fight on the flight back from Polokwane.
“That’s absolute nonsense,” Domenech said when asked about that report. “Those who know Yoann a bit know it is totally impossible for him to fight with anybody.”
France’s fate is now out of their hands and even a big win over South Africa in their final group game in Bloemfontein on Tuesday might not be enough for them to survive the group stage.