Until you closed with New Balance and Asics not working or no longer producing the shoes you need, my advice was going to be to check the Spanish websites for both. For what it is worth, here they are:
New Balance -
http://www.newbalance.es/es/stores
Asics -
http://www.asics.com/es/es-es/
Both sites have a store locator you can use to locate a vendor in one of the major large towns or cities along the way. Others have correctly stated that you can find shoe vendors (generally) at Pamplona, Logrono, Burgos, Leon, Astorga, Ponferrada, Sarria, and Santiago de Compostela.
However, I suspect you particular situation is going to be more problematic. The width issue is going to severely restrict the availability and selection, even if you DO find a source in Spain.
All said, my 'best" suggestion for you would be to bring a second pair with you on the plane. You have two choices for "forward deploying" them:
1. (My recommended choice) Make a reservation at a hotel about where you think you will need the shoes. Send an e-mail (use Google or Bing Translate) to ask the hotel if they will accept and hold a parcel you will mail to yourself care of (c/0) the hotel. If they will, then you simply mail the extra shoes to this address, perhaps with your name and reservation number in the lower left corner so the hotel will notice it when the parcel comes. You can send the shoes from a post office in France before you start form Le Puy, to a Spanish address with no problem. The French postal system is a bit more expensive than the Spanish system. However, your parcel should arrive before you do.
OR:
2. Send the shoes ahead to a post office (Correos) by way of general delivery (Post Restante). There are prodigious instructions on how to do this here.
If you thought you would need the shoes by the time you hit the halfway point on the
Camino Frances, this would be Leon. The actual mid-point is closer to Sahagun (before Leon) but Leon is the nearest city with shoe stores and more than one post office, as well as hotels to reserve at all price points.
I hope this helps.