Interestingly I do not stutter in French or any other language nor do I stutter when I put a voice on (acting or whatever). I only stutter in my native tongue (English). That said my French probably makes no sense to people anyway... Have you tried an app or something where you can go at your own pace? I think the key will be to get used to the parts you stutter on and find a way around it which is hard as you are learning rather than just speaking the language as you wont have any bridge words or alternative words to use just yet to help you out. You will get there though eventually.