I suppose there's reason to believe they were romantically involved, though perhaps *after* she came of age?
If I recall correctly, a member here, maybe Mon Maquis, had mentioned that after Alizée left MF/LB and went on her hiatus, Olivier was spotted supporting a different artist as a manager. I think it was Natasha St. Pier. I could have sworn I also saw pictures of these two together. For that reason I think it's fair to say that he really was her manager. Again, they may have been "involved" but perhaps only in private and for a short time.