The twin engine Casa C-295 was returning to Algiers with a cargo of banknote paper for the Bank of Algeria, sources told the AFP news agency.
A military statement said that it was delivering “equipment” from France to the bank.
It burned for about an hour after crashing near the village of Trelans in the Lozère, France’s most thinly occupied department which is about 1,000 metres above sea level.
Although conditions were foggy, Trelans mayor Bertrand Cayrel said that he heard a loud noise and saw the plane apparently jolt before falling to earth in a cloud of smoke.
Five military officials and a Bank of Algeria representative were on board but rescue workers only found one body in the cockpit and three in the cabin, which has separated from the front of the plane.
One witness said he thought he saw a parachute in the sky but a source close to the investigation said that it was a piece of the cabin.
Rain and lowlying cloud hampered the search on Saturday, preventing helicopters from taking part, but 80 police officers were helping rescue workers search for the missing men.
Two other teams are extracting the bodies from the wreckage and searching for the plane’s black box.
Algerian officials were at the scene on Saturday, journalists reported.