Police opened fire on the car, failing to stop it from speeding away after the incident in the Place de la Concorde at the foot of the famous Champs Elysees.
The car was later found abandoned nearby.
A police source said witnesses saw two men and two women leaving the bullet-ridden car.
The world's greatest cycling race was to finish layer today at the Arc de Triomphe, at the other end of the Champs Elysees, after the cyclists perform several laps up and down the famous avenue.
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No one is believed to have been hit as the police shot at the car, and police stressed that no shots were fired from the car.
Security in the French capital has been heightened for months following jihadist attacks which claimed 17 lives that began with the massacre at the satirical weekly Charlie Hebdo.
British cyclist Chris Froome was set to win the tour, and thus secure his second victory, barring an unforeseen disaster.