Hmmm... I'll submit it here in case an admin see it. If there's no answer I'll submit it again in the beta forums.
Basicly, it's related to the librairies path (My Documents, My Pictures,etc).
In the french version of Windows, "Librairies" is called "Bibliothèque".
Basicly, I moved my librairies on my D: drive, since my C: drive is a small SSD. So I created the folder D:\Bibliothèques\ to put everything.
The problem comes from the "è" letter, which is not a standard english letter. It would seem FFXIV didn't like it. Instead of saving its data in D:\Bibliothèques\Documents\My Games\FINAL FANTASY XIV\, it created a new folder and saved everything under the folder D:\Bibliothèques\Documents\My Games\FINAL FANTASY XIV.
Here's a screenshot to help you understand :
Edit : If I noticed it today it's because I decided cleaning my hard-drive today.
Considering ARR should be rewritten from scratch, maybe it will be fixed anyway.