Thank you for your question. I am sorry for the delay, due to the fact that there are only a few EU law experts on the website.
To answer your question, you can only claim French citizenship, which you would in fact receive automatically, if your father would recognize you legally, therefore changing your father's identity on your birth certificate, probably judicially, because the courts would have to recognize this change in paternity. Once this happens, you can apply for French citizenship as a person born of a French father at the time of your birth.
Unfortunately, no other means of action is available, if you wish for automatic citizenship. Of course, you could apply for naturalization like any other person considered a foreigner, but it would be much more of a complication, since citizenship by birth does not require knowledge of French, residence time etc.
I hope my answer is useful and look forward to your rating, which is essential to my activity.
Dr I L Vlad