Ciao tennisjr,
Sounds like a wonderful vacation! You can definitely get around Rome without a car.... and actually would recommend it because I've heard driving in Rome can be a real nightmare, particularly as far as traffic and lack of parking goes.
So I'd recommend staying central, moving around with bus, metro or walking.... then take train to either Florence OR Pisa, and rent a car for your stay in Tuscany.
Here are some tips for car rental from Florence and for Tuscany:
http://www.discovertuscany.com/tuscany-car-rental/
http://www.visitflorence.com/florence-car-rental/
Then return your car in Pisa at the international airport there. It makes more sense to fly to Paris, the time you save is definitely better used seeing Paris your last 3 days.
If you have any other questions, feel free to post! In the meantime, HAPPY NEW YEAR 2013!