The pilot and all 10 passengers - five students and five instructors - died in the accident, the prefecture said.
The French interior minister was on his way to the scene, the interior ministry said.
Yves Seguy, the regional prefect, told broadcaster BFM the aircraft appeared to suffer damage before plunging vertically to the ground.
The crash occurred in a built-up area near a shopping centre.
"Give or take a few metres and the accident could have caused collateral casualties," Seguy said.
Flight tracking sites identified the plane as a single-engine Pilatus PC-6, a small transporter of freight, passengers and skydivers.
Emergency services responded immediately and were providing psychological support to several relatives of the victims, Seguy said, adding that authorities were also collecting witness statements.
"We are deploying all available resources," he said, including emergency medical teams, fire services, police and mental health support.
A resident, identified as John Curaku by BFM, told the broadcaster that he was in his garden when he heard what sounded like a plane's engine stopping, immediately followed by a bang.
He said he went to the crash site and "there were no signs of life," with two of the bodies thrown a few metres from the plane.
with AP
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