The
Camino Francés won't be any better! Perhaps if you move ahead and go to the
Camino Primitivo - away from the coast, you might find less accommodation racing. August is definitely the worst time to try to get accommodations without a reservation because as
@trecile mentions, it is high season throughout Europe and Spain's northern and southern coasts are very popular!
My only recommendation would be that before you leave where you are right now you call ahead to try and find out if you can reserve. You might have to try private
albergues,
pensiones, casas rurales and, of course hotels, just so that you know that you'll have a place for the night and not worry as you walk during the day. Perhaps you could consider towns in between, or going further using public transportation to where you might find lodging.
Buen Camino!