The 30-year-old completed a season-long loan switch to the Stade Velodrome after the former Hoops manager Mark Hughes deemed the midfielder surplus to requirements.
Barton made his first Ligue 1 appearance in a 1-0 victory over Lille after serving a 12-match ban for violent conduct after he was sent off in a 3-2 loss to Manchester City in May.
The England international has been one of Marseille’s best performers this term, inspiring the club to a 2-1 win at Brest, while scoring against Borussia Mönchengladbach in Europe.
Anigo has been impressed by Barton’s effortless transition from the west London outfit to Marseille, and he hinted the former Newcastle United man could have a long-term future at the club.
“He was described as an animal, but he is just the opposite. He is funny, intelligent, and he fights for victory,” Anigo told L’Equipe.
“We can see that the team has been lifted by his competitive spirit. He is now established as a leader in our group.
“He is very happy here, maybe he has found the right club for him. Should he desire (to stay) it could be very good. We have a very good relationship with his club QPR.”
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