Depends which nation. Some of the Belgian, French, and Dutch army remnants were evacuated at Dunkirk with the British and fought with the English. Poland's army surrendered, they went home basically. Denmark's army barely existed in the first place. Norway also laid down their arms. The rest of the French army laid down their arms. Vichy France continued to fight in north Africa against the Americans until admiral Darlan's surrender in 1942. The Greeks were partially evacuated to England as well and fought in d-day. The Baltic countries resisted but not successfully. Surrender of the nation means disbanding of the military in most cases and unless they could be evacuated the army just went home. Some may have fought in resistance battles but never as a national army. Some may also have chosen to join the German army.

Sources:

Blood, tears, and folly Len Deighton