The former Manchester United striker scored twice on debut in victory over Los Angeles FC last weekend.
Alessandrini told France Football: "How do you train with him? Madness. Thursday, for his presentation, there were a lot of journalists. It's good for the club, for the city for football here.
"And for me? Last season, I gave 12 assists. With him, I hope to succeed even more. What's the point of wearing the same jersey when we've always been an opponent? You forget. You look at the player and the character, and you savour. Especially since he spontaneously came to talk to me.
"What did he tell me? He asked me how it happened at OM, how was the MLS, we discussed Paris. He spoke to me in French, I was a little impressed..."