I hope you are not trying to beat the system as it is illegal to stay in Japan beyond the visa period. Japanese immigration will have that record in the system the next time you try to enter Japan again. I have heard cases before.
It is better to follow the advice above. Enter Japan with a round trip ticket or you may be asked a lot of questions at immigration. If you manage to secure a student visa or a working visa before the end of your 3-month language stint, then it is ok. Previously, we need to have a Japanese to be our guarantor to secure our student visa. Not sure about now. If your visa should expire before the next visa is approved, then that trip to another country and back into Japan will come in necessary. Take it as a self-granted holiday.
If as you say you are going to Japan to be with your Japanese fiance, I assume that she wants to stay in Japan. Then, if she really wants you, you can both tie the knot and apply for residence permit.
Ken