The most economical tourists can walk to the city center. It will take about half an hour.
The second 'most economical' option is to take the bus. There are buses Chronoplus to the center of Biarritz. The price of a ticket valid for 1 hour is 1 EUR (you can buy at kiosks or from the driver), a day ticket will cost twice as much - 2 EUR..
And finally, the third option is a cab. The approximate cost of a cab ride from the airport to Biarritz is 60 EUR. Travel time is 10-15 minutes.