The excellent Meteoblue.com weather forecast website lets you see a detailed forecast for Saint-Jean-Pied-de-Port as well as for the top of the Valcarlos route (enter Puerta de Ibañeta) and for the top of the Napoleon route (enter Col de Bentarte). I learnt about this website because the Pilgrim Office in SJPP used to print out their forecast and put it up on the wall in their office; I think they have now switched to a different provider. The volunteers won't know the weather forecast any better than these weather services but what they do know, and what you can only learn from them in early April, is the condition of the path on the ground.
Just by way of an example, you can see that, today, SJPP will enjoy temperatures of up to 22 ºC (72 ºF), while the temperature on the two passes will no climb above 14 ºC (57 ºF), and next week they expect it to be considerably colder with rain mixed with snow or even only snow on the high Bentarte/Lepoeder passes while it will rain in the town of SJPP and on the low Ibañeta pass.