I have finally discovered a concrete linkage between the name Foy and Fay both originating in FRANCE. The evidence is in a modern day website from which I translate.
The people or inhabitants from La Foye Monjault are still called "les Fayais". It seems conclusive, then that the Feys and Foyes are those people from this area.
La commune de La Foye Monjault compte 695 habitants appelés "les Fayais". Sa superficie est de 1 900 Ha, et elle est située à 15 Kms de Niort, 80 Kms de Poitiers, 30 Kms de St Jean d'Angély et à 50 Kms de La Rochelle.
The community of Foye Monjault numbers 695 inhabitants called "Les Fayais". Its area is 1 900 Hectares.It is situated 15 Kms from Niort, 80 Kms from Poitiers, 30 Kms from St John d'Angély and 50 Kms from The Rochelle.