I would expect the weather would be fine for camping. I did the opposite direction from Roscoff in France to Alicante a couple of years ago beginning in early April. I only had one cold night in northern France waking up to find frost on the tent. I was perfectly snug inside with an Alpkit Pipedream 400 sleeping bag. I had a couple of nights in cheap-ish Ibis hotels but that was more a function of arriving in a big town at night or it peeing it down all day than the cold. I went through Pamplona, Zaragoza, Teruel, Valencia and didn't find many campsites though that's not exactly the most touristy of routes. Most are essentially trailer parks. Turning up with a bike and a tent is seemingly unusual. France is much more tent friendly though that early on and you're possibly out of season for the municipal camp sites.