The accident happened shortly after the plane took off from a strip 70 kilometres (40 miles) from the city of Metz in the Moselle region.
For a reason not yet determined the plane "turned at a right-angle, crashed into a field and immediately burst into flames", the local authority said.
Pakistan Army aircraft crash-lands near Peshawar
Two men, aged 50 and 18, died in the accident and their bodies were recovered by investigators after several witness alerted the authorities.
An air transport police enquiry has been set up to determine the cause of the crash.
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