Are there luggage storage or lockers in Biarritz, either in the city center or in the train station?
According to the SNCF web-site there are 15 stations in France which offer left luggage facilities and Biarritz is not one of them.
The page is in French but the list of stations is clear enough. Note that two of them offer a manual office the others are automatic lockers.
If you search for Biarritz consigne you will find there are commercial enterprises offering left luggage in Biarritz but since I have never used one I will not provide a link to a specific service. Be careful you do not find a restaurant called La Consigne by mistake.