We're flying into Carcassonne and then out of Barcelona.
I have driven from and to Perpignan/Barcelona and as previously mentioned it's a trek and a half, I'm also aware of price hiking in regards of travelling across the borders of France and Spain.

Pros of car hire; instant access and own preference as to when and where to go.

Cons of car hire; pain in the ass to drive abroad, parking in some areas is very restrictive, can be more expensive in the long run, traffic jams and stress.

I haven't driven in France for the last 5 years due to the above, preferring to use the excellent transport facility's they have abroad. Having travelled across most of Southern France by train I would not do it any other way.

Flying to Barcelona on Friday 14th, car hire already booked, usually drive when abroad and never had any problems. Motorway is pretty good but several stops to get through toll booths and the Spain / France border usually has a queue which will delay you about 15 mins. Were reckoning on a journey of around 2.5 hours to get to Perps which subject to the flights taking off ok next week should see us on the pop in the Castillet bar around 2pm. Two nights in Perps then back over the border into Spain (far, far, cheaper) for 3 nights.

Cons - Personally never pay the full damage waiver they try and sting you for at the airport when you pick the car up, you've paid up front and you think thats it (you have basic damage waiver) but then they try and put the frighteners on you to take a belt and braces insurance package.

Pros - freedom to travel when you want and where you want especially if your there for a few days

I found the best and one of the cheapest ways to get to perpignan was the train! But I know that there is a shuttle service from the Airport to Perpignan.

The last time I went into to Montpelier and out at Carcassonne and the train was just under 20euros each for a 2hour train journey.

Hope this helps!

I live in Girona (between Barcelona and Perpignan) so I should be able to help on this one.
If you are flying to Barcelona there is a good rail service (renfe) to Perpignan but be careful about times coming back as there are not as many trains on Saturday night or Sunday. Will be cheap and very clean but can take a while as there are quite a few stops.
If you don't mind not drinking, car hire is more convenient. You can hire in Barcelona for good rates, very competitive at this time of year, but be careful of the insurance. If you hire a car more than once a year take out an annual carhire excess policy usually about £40/annum, then you can go with the basic car hire insurance. Also, they will probably charge you extra for taking it across the border to France.
It is a long way but most of it is on the toll road so you will make good time.
I always recommend people fly to and from Girona if possible as it is a shorter trip (by car, bus or rail) on the day of the game and the city itself is very nice for a long weekend or convenient for staying on the Costa Brava if you are making a week of it. If you want to stay in Barcelona that is no problem as the bus laid on by a partner of Ryanair goes from Girona to Barcelona, taking about an hour, which is less time than it takes to get to Barca centre from the Barcelona airports!
If you want more detailed info, I would be happy to receive a private mail with more help.
I am now getting ready for the Barcelona Grand Prix weekend - no sunscreen unfortunately, only a good raincoat - hope the weather improves for next weekend.