So no worries for getting from Bayonne to SJPP by public transport. There's been a landslide, trains will run as scheduled from Bayonne to Cambo-les-Bains where a bus will be waiting for the passengers from the train to take them to SJPP. The whole train+bus journey from Bayonne to SJPP will last about 1h 20 min. Departure from Bayonne at 6:41, 8:50, 14:35, 17:09 and 18:35.
All as announced on sncf.com. This arrangement is currently foreseen until August 30. You can also check it on the real-time board of arrivals and departures for Bayonne station where (at the time of writing this post) the first connection to SJPP at 6:41 is already on the board - with no cancellations:
https://www.garesetconnexions.sncf/fr/gare/frxby/bayonne/transports-horaires/liste
Buen Camino!