rental cars ...one way

Drop your Italian car in Italy, cross the border, and re-rent. Of course, you would have to do this at each border, but since you apparently wish to drive that is the only option for keeping cost down. Otherwise, you could fly.

Fly on one of the lo-cost inter EU airlines that you will find on Whichbudget.com or Skyscanner.com. Watch the airport location and bag and weight restrictions. Or rent in each Country, or return it to the same. Rail or bus to the next Country, pick up your rental, then drop off and rail or bus to the next, etc.

Check the Vueling website. They are a very respectable budget line, which flies between Venice and Barcelona. I can't see why anyone would drive unless they had a phobia about flying. In that case, I believe San Remo is the westernmost city where you could drop a car and get a train to Nice. We did it once, about 9 or 10 years ago, so things may have changed; but it was very easy. We stayed overnight and caught an intercity train the next morning. Find out at which southwestern French city you can drop a car, and do the same. Get the train to Barcelona. Unless you want to see some of the places on the way, I can't see why you would let yourself in for such a very long, expensive drive. Figure the rental charge, gas ($9/gal), and quite high tolls in Italy and France.

Vueling Airlines is the only way to go.
Some of the distances across Europe are pretty far, and flying a budget air carrier is the way to go. It can actually save you $, too.

Hi Guys, I agree that the fastest method to get to Barcelona would be by flight! However, our intention is to travel from Venice through Florence-San Gimignano-Cinque Terre and Portofino stopping and in small spots along the way. We will do the same in France and Spain as well. ..will check out the drop at border option
.....any other ideas?

I think renting a different car in each country is your only option if you wish to avoid those large drop off fees.

Yes, plan to drop close to the border (preferably at an agency next to a train or bus station). Train or bus across the border and pick up another car. You run into higher rates this way, if you don't have it for more than a week, but it's going to be significantly less than the cross-border drop-off fee. If you are creative, you may also find you can avoid keeping a car during city visits. In a city, a car can be an expensive hassle - you have to pay to park it, whether you use it or not.