R reservations needed crossing the Pyrenees middle of June on way to Bilbao?
Reservations for what? It’s an open border between countries, if you’re traveling between countries, and you don’t state where you’re coming from or going to.
We made hotel reservations a day or two ahead in June due to weather concerns. We drove on the French side as the highway was closer to the mountains.
We were traveling from Hondarribia, Spain to Collioure, France, then to Barcelona.
If you have a car and are somewhat flexible about what town you stay in (in case you encounter a special event that soaks up every room in one town), I think you'll be OK if you book something the night before. It would be a bit riskier to do it day-of, and the conservative folks would recommend keeping an eye on the options available (I use booking.com) at your probable first-choice destination from 3 or 4 days out so you'll have some warning if you're heading into dangerous territory.
I traveled in the opposite direction in late May last year and crossed at a different point. I ran into a problem in the French town of Pau. Had to pay a lot more than I liked but was using public transportation and didn't have much flexibility. It turned out there was a classic car race going on. Would have been fun if I had any interest in that sort of thing. I've also run into a couple of bike races that caused lodging issues and some sort of festival in Arles that must be very popular, because it affected lodging as far away as Avignon. Again, life is a lot easier if you have a car. You can even look for a place to stay out in the country.