I would say that the difference lies in what is modified by finalement. In the first case, it modifies tourner vers le français, so it means that after some time, you chose French.

On the other hand, if it is in initial (or final) position, it modifies the whole sentence, and in that case I would understand that at first you weren’t happy you chose French, but that after some time, your opinion changed and that now you are glad you chose it. By the way, I suspect that the same distinction exists in English.