Biarritz is a seaside town in the Southwest of France, near the Spanish border.
East towards Toulouse
There is a great and cheap bus system in the whole area of Bayonne, Biarritz and Bidart! A onewayticket is just one euro, no matter how far you go. Its valid for one hour! A 24 hour ticket is two euro, so well worth it.
To hitch in direction Toulouse take the bus C in direction St Pierre d`irube and get off at the stop Dasbendia! The bus stop is just before a roundabout! Following the signs to the motorway you have to go left! Its a walk of less than ten minutes! You will pass a college on your left side and soon arrive at the next roundabout which leads to the A36 to the right. The cars see you and there is enough space to stop!
Going South (Portugal, Spain, etc.)
I got a lift off a car driver on the Boulevard Marcel Dassault just South of Biarritz (less than 1 KM from the airport). There are many roundabouts on this road leading to the A63 Motorway. It took me 5 minutes to get a ride. There appears to be a lot of international traffic in this region.
Otherways there is a gasstation at the highway a bit south from Biarritz at (43.423196,-1.597749). It's pretty easyly reachable by taking the bus 13 from the center heading Bidart. From the last stop (43.430482,-1.598863) it's just a fifteen minute walk to there. I recommend to check the route out on google maps before and take a screenshot.