Visa requirements for Camino

Neither the U.S. nor Ireland are Schengen countries, so you are limited to a 90-day stay without a visa. For a longer stay, you need a Schengen visa from the country in which you will reside. Your current residence does not matter for visa purposes. Pick your favorite passport for traveling!

Ireland is not a Schengen country but its citizens are part of the European Union. With an Irish passport you need to have your passport to enter Spain, but you do not require a Visa, and don't have the 90 day Schengen limit.
Margaret

Ireland is not a member of the Schengen area, so neither of your passports will give you any specific advantages entering France or Spain.

The US State Department information page on visa requirements is at http://www.immihelp.com/visas/schengenvisa/. It indicates that if you were to travel on a US passport, there is no need to apply for a visa, but will have your passport stamped on arrival. Entry is still (always) at the discretion of the passport control at the point of entry, but unless there is something unusual, this is normally a formality.

It appears that the same arrangements apply for Irish citizens, although most of the sources I can find are at best secondary (eg commercial visa application services).

Regards,