The aircraft, operating from Nancy-Ochey air base, crashed late Tuesday in the Meurthe-et-Moselle department near the city of Nancy, according to French broadcaster BFMTV.
The two-member crew consisted of a pilot and a navigator.
Authorities confirmed the pilot's death, while search operations continued for the missing navigator.
The crash occurred around 11.35 pm local time (2135GMT) in an area between the villages of Rogeville, Domevre-en-Haye and Tremblecourt, north of Nancy.
Henry Lemoine, mayor of nearby Pont-a-Mousson, said substantial police and firefighting resources had been deployed to the area.
Debris from the aircraft was located by a drone, but authorities had not provided further details as emergency operations continued, Lemoine said in a statement on Facebook.
A crisis coordination center was established in Rogeville, while local authorities warned of possible traffic disruptions in the surrounding area.
A judicial investigation has been opened to determine the circumstances and cause of the crash.