As a native French, I can say we don't use this word: fangirl, not even: fanboy. Or at least, I never heard them here..
If you are talking about an obsessive female fan, who likes / loves something to an excessive level, so we say:
_ Il est obsédé par ... ( He is obsessed by .... ). Example:
Il est obsédé par Nicole Kidman / He is obsessed by Nicole Kidman.
_ Elle est obsédée par ... ( She is obsessed by..... )
Elle est obsédée par Lionel Richie. / She is obsessed by Lionel Richie.
If you are talking about a fan, like for example: fan d'un chanteur, d'une actrice ( fan of a singer, of an actress ), but in a normal way ( not obsessively), so we also use the word: Fan, but alone. Without ' girl' or ' boy' at the end.
Another example: Je suis fan de Mariah Carey / I'm a fan of Mariah Carey.