Another eyewitness told BFM TV how he saw the vehicle "drive through an automatic gate at the terminal, making a deafening sound in the process".
The dramatic chase was captured in an amateur video posted on social media.
The vehicle hurtled across the restricted runway area with police cars and a helicopter in pursuit following a chase along a nearby motorway, a police source said.
There, he rammed into automatic glass doors near the main entrance to Terminal 1 and drove through the building.
The suspect then abandons the auto, and is surrounded by officers, who later arrested him.
The driver first broke through a security barrier at the Lyon-Bron business airport before changing direction and heading to Lyon's main Saint-Exupery airport about 20 kilometres (12 miles) away.
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The Lyon prosecutors' office is investigating possible charges of attempted murder against the suspect.
The majority of flights for the rest of the afternoon have been cancelled from Lyon Airport, with such airline as Air France and HOP! particularly affected.
Local government press officer Christelle Monteagudo said the man's motives were unknown and that nothing was being ruled out.
The driver jumped out while the vehicle was still rolling and sprinted off on foot, pursued by a police van.
An amateur video on social media showed the auto being chased by several police vehicles.
Flights at the airport were grounded.
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