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.