Before driving onto the runway the man had driven the car into the glass doors of one of the airport terminals.
Nobody was injured in the incident, which led to the suspension of all flights in and out of Lyon Saint-Exupery airport, situated in the east of the city.
A police source said the man's motives were not yet known.
Officials said that earlier the man smashed through a security barrier at Lyon-Bron business airport, about 20 kilometres away, before turning back.
The vehicle was also seen speeding the wrong way along a motorway.
An AFP (French news agency) journalist who was waiting in one of the planes on the runway saw police vehicles pursuing the man.
The pilot told passengers that the delay was due to a helicopter being dispatched as part of the pursuit.
An amateur video on social media showed the car being chased by several police vehicles.
The motorist then abandons the vehicle and continues on foot, weaving his way past several cars before being wrestled to the ground by officers.