Before you go any further, look into the price of picking up a rental car in Paris and dropping it in Barcelona, and then look at the price of picking up a rental car in Barcelona and dropping it in Paris. Look at Kayak, Gemut, Kemwel, and AutoEurope.
When you see this, you will probably want to rethink your plan. The starting and ending cities aren't the problem, it's that cars rented in one country and returned in another have a surcharge. On this Forum, I've seen reports ranging from €50 to €600 (not a typo - six hundred euros).
If you don't want to pay this fee, you'll have to come up with a different plan, such as taking a train across the border, or flying from one to another, or limiting yourself to one country. With only ten days, you'll find plenty to do in either country.