The 30-year-old, who still has nine games to serve of a 12-match ban, made the switch to Ligue 1 last month.
"So far, so good. It's not normal [at the moment], because there is no match. But what is important is the competition. We'll see when he can play the games. He is very friendly, very open and smiling," Baup told Mediafoot.
"He wants to do good things with us. I've never asked the question [if he may slip up]. I only think about the game and the integration of the player. I think about [in] what position he will be most useful."
Barton will spend at least one season at Marseille.