Enemy, foe denote an individual or body of individuals that is hostile or that manifests hostility to another.
Enemy usually stresses antagonism that arises from a cherished hatred or a desire to harm or destroy, but it may suggest nothing much more than active or evident dislike or a habit of preying upon.
Foe, on the other hand, implies active warfare.
When the reference is to a nation or group of nations with whom a country is at war, enemy is preferred in general use, foe being used in this sense chiefly in poetry or rhetorical prose.