The crash killed five instructors, five students, and the pilot, said Yves Seguy, the prefect of the eastern department of Meurthe-et-Moselle.
“There were no bystanders among the victims,” he added, speaking at a press conference.
The aircraft, registered in Germany, crashed in a grassy area near the runway of the Nancy-Essey aerodrome, close to a residential area and two roads, an AFP journalist reported.
The cause of the incident was not immediately clear.
Medical and psychological support teams were caring for relatives of the victims who were present at the airfield, as well as other witnesses.
A technical investigation had been opened, said Amaury Lacote, deputy public prosecutor in the eastern city of Nancy.
Police urged people on the social media platform X to “strictly avoid” the area around the airport to allow emergency services access.
French Interior Minister Laurent Nunez is expected to visit the scene of the accident in the late afternoon, according to his staff.