I know my father's ancestors lived in the French Pyrinees, but I don't know what towns that can include. His last names: Etcheverry Etchegoyen Ezquiaga Curuchet.
Does anybody know which towns or cities would be considered to be in this region???

There are going to be many, many towns in that region.
The Basque Country consists of 4 provinces in Spain and
3 provinces in France. You may want to get yourself a map
of that area. Each province has hundreds, even thousands of little towns in it. You might want to visit a site like
Buber's Basque Page to get familiar with the Basque Country.