I prefer Maximilienne to get Max (which is utterly adorable) as a girls' name, but I recognize it's pretty OTT. I just don't like the sound of Maxine. Most -ine names don't do it for me, Maxine is no exception. It feels clunky in spite of being short. That said I would vastly prefer Maxine to trendy names like Paisley or even Sophia which is getting pretty tired in spite of being a classic.
~Anna~