You can find good info regarding your answer here:
it's in french but you should be able to read it.
Anyway, the answer is yes.
You can enter Italy with your french titre de sejour, as long as you don't stay in Italy for more than 3 months.
If in the meantime you will obtain italian "permesso di soggiorno" no problem at all.
Having said that, it's not very clear if you will come to Italy from France or from Turkey. Or where you are staying at the moment. Because if your italian permesso di soggiorno expired "some months ago", and you are still in Italy, probably you are violating the law.