Way too ambitious.
First of all you need to know that if you pick up a rental car in one country (Italy) and drop it off in another (Spain or France) the drop off fees range from 400 to 600 euro, so probably more than the entire rental charge. So keep that in mind.
In these cases it's best to drop the car off at a location within the country, near the border if possible, proceed by train to the next country and, if necessary, rent another car there.
But the other issue is time. 7-9 days are barely enough to see Tuscany and the Cinque Terre. For example Venice, should take about 3 nights (that's my recommended length of stay there). Tuscany will take another 3 just for the country side, but if you want to include Florence, then you need at least 5 in the region of Tuscany. The Cinque Terre, at the very least 2 nights. So there isn't much left of your vacation. Consider that driving to France (assuming you don't care to spend 500 euro in drop off fee) is a long way. From Florence to Montecarlo (which I used to drive a few times when I lived in Florence) was a 5 hr trip, with no stops and at a good speed. I've never driven to Barcelona from Florence (only flown, a few times) but some of my friends have. It's a 10 hour drive at very high speeds on the freeway with no stops except for gas.
I think with 7 to 9 days, you should limit yourself to Venice, Tuscany, Cinque Terre. Rental car is recommended for the Tuscany countryside and small villages, but totally unnecessary (actually a hassle to have) in Venice, Florence and Cinque Terre. Therefore pick up the car when you leave Venice. Go and do the Tuscan country side first. Then drop the car off in Florence. Stay in Florence without a car, then go to the Cinque Terre by train, where you won't need the car at all either.
Alternatively you can stay in the countryside of Tuscany iwth a car, but visit Florence from there (on day trips). Don't stay in a Florence hotel with a car. Then drive to La Spezia (near the Cinque Terre) return the car there and take a short train ride to the Cinque Terre. Then take a train to the airport where you depart from (Pisa is the closest, otherwise Milan or Rome, the largest, are only about 3-4 hours away by train.