I've done a bit of riding in the western Pyrenees but not a full on tour. Have used these cycle tourist maps as guides. They may be of interest. Guide velo from
www.tourisme64.com is a bit simplistic but wil give you a good idea of popular routes with cyclists and Navarra en bicicleta from
www.turismo.navarra.es shows some popular routes on the Spanish side of the border. Col profiles are available in lots places, the one I use most is climbbybike.com. My favourite way to cross the border is to follow the river nive from Bayonne, gentle climbs up to Cambo-les-bains then tips up a bit but never seriously pointy to st jean pied de port. You then have a choice of crossing ponts, col d'ispeguy, col d'urquiga or puerto d'ibaneta. The descent from roncesvalles into navarra and Pamplona is spectacular. Only problem with this route is its popularity, depending on the time of year it can be swamped with pilgrims walking/cycling/crawling the casino Frances and the the route to Santiago. I stress I have not cycled these route fully laden. If you do decide to cross further west, I would recommend the old smugglers route, la route des contrabandiers around esplette and ainhoa. Beautiful basque villages and the most breathtaking scenery. Only problem is it doesn't really get you across the Pyrenees and as others have pointed out, the fun really starts when you get to Spain. Hope this helps and good luck.