Are you aware that the higher level route through the Pyrenees from SJPDP to Roncesvalles is officially closed between 1 November and 31 March? You risk heavy fines if you walk the Route Napoleon during that period. The lower Valcarlos route remains open year round, is relatively straightforward and is close to a major road for much of its length.
Weather - you could find almost anything. The route covers a wide range of terrain and elevations. Websites like Weatherspark will give detailed historical averages but the reality is that a few days of abnormal weather like the high winds and rainfall of the past few days may completely alter your experience. Walking at any time I would come prepared for persistent heavy rain. In November and December in the higher areas you can expect to encounter snow and sub-zero temperatures overnight and in early morning. Be prepared to dress accordingly. I strongly suggest lightweight gloves for use on cold mornings.
In Pamplona, the summers are warm and mostly clear and the winters are very cold and partly cloudy. Over the course of the year, the temperature typically varies from 33°F to 82°F and is rarely below 23°F or above 94°F.
weatherspark.com