Other police vehicles and officers on foot then tried to cut off his escape until one of them managed to catch up with the suspect and wrestle him to the ground, the video showed.
France's Lyon airport halted flights on Monday when a driver being chased by police smashed his auto through a terminal building and onto a runway.
He said: "An individual drove his vehicle onto the runways at Lyon airport!"
Local government press officer Christelle Monteagudo said Monday that the man's motives were unknown and that nothing is being ruled out at this point.
Flights were grounded until further notice, the airport tweeted.
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An amateur video on social media showed the auto being chased by several police vehicles.
Radio Télé Luxembourg has reported shots were fired by police at the scene.
Before driving onto the runway the man had driven the vehicle into the glass doors of one of the airport terminals.
Lyon Saint-Exupéry, France's third busiest airport, was closed and about 50 flights cancelled after the man, in his 30s, smashed through a security barrier today and drove through the terminal, on to the airport apron and then the runway. The chase lasted only a few minutes, but it was enough to disrupt operations at the airport.