You’re in what you’ll probably remember as the least interesting part of your trip TJ, the roads are long straight, demoralising and dangerous. The coastal cycle route is just as demoralising but has the merit of being safe. All I can suggest is seeking out small roads that don’t link the major settlements.
When you break out of the forest just before Bayonne you exchange people flying along the long staight roads through the pines for irritated urban drivers. The Basque coast between Bayonne and St Seb is highly populated and hectic, if you take that route it’s best to take the cycle route around the coast to Hendaye, the roads are awful. In Spain the Camino bike route goes up and down a lot but the alternative main roads are not bike friendly.
The other posibility is going through the mountains, for example making a bee line for St Jean Pied de Port and over to Pampelone following el Camino Frances bike route to Estella. It goes over the Col de Ronceveau but the total climbing isn’t any more than the constant up and down along the coast.
Godd luck whichever way you go and stay alert when being overtaken on those long straights, it’s the part of your journey you’re most likely to be run off the road. 🙁