As an FYI, car rental in Europe is a million times worse than my experiences in the US. I would be very motivated to try another way to do it. It is totally normal to have a 1-2 hour wait in the UK or France at most airports, for example.
The thing I've always found though is that off-season in EU is _way_ cheaper than US. Went to Italy last month, 1 week for a medium sized car was something like 100 euros. And it's not unusual to rent a car for ~6 euros per day.
Trick is to stick with one company, avoids the registration as a new customer.