The French news agency AFP quoted the news agency as saying the crash happened shortly after takeoff from Versailles airfield near Grenoble in southeastern France on Saturday afternoon.
Witnesses said the bodies of four adults and a child were recovered from the wreckage of the burnt plane.
The French rescue agency said the plane caught fire after it crashed.
Sixty firefighters were called to the scene to put out the blaze.
Grenoble prosecutors have already begun an investigation into how the plane crashed.
Meanwhile, the Daily Mail reported that one of the dead was a pilot.
The other four are believed to be from the same family.
However, details about their identities are not yet known.
The small tourist plane crashed into a village about 650 meters above sea level, local Australian media reported. The exact cause of the accident is not yet known.
In June last year, a small four-seater plane crashed near the northern French city of Lille. Three people lost their lives in that accident.