I would echo the cautions and advice of lancebanyon and cbn42.
There are a number of hotels around Frankfurt Airport that you could check-in to for your first day to give yourself 24 hours to acclimate and get some sleep. Or you get a room in Frankfurt, itself. No more than a short train journey away.
It sounds like you are going to Europe for the first time and renting a car for six weeks, and of that time, the car will be parked for most of that period?
Why are you incurring that unnecessary expense and headache of driving?
Are you renting a manual car or an automatic one?
The latter are much more expensive in Europe.
Also, you want to eat McDonald's in Europe? Why?
Also, you are staying outside Rome ... how far outside?
I can understand your desire to take a nice long vacation and use miles/points to cover airfares and hotels, but it seems to me you are not setting yourself up for a wholly successful trip here.