Police in central Paris shot dead two people on Sunday night, firing on a car that was trying to hit them, a police source told AFP.
The vehicle was driving against the flow of traffic on the Pont Neuf when it sped towards the officers, who opened fire, according to the same police source.
A security perimeter had been set up at the scene in the heart of the capital where a judge was expected to arrive.
France's police oversight body, the General Inspectorate of the National Police, is also expected to be deployed, as is typical following an officer's use of a firearm.
The motive behind the incident is unknown. It took place hours after exit polls from the second round of the French presidential election found that President Emmanuel Macron will defeat his right-wing challenger, Marine Le Pen, by more than 16 points.
France has been hit by a number of terrorist attacks in recent years, the biggest one being the attack in November of 2015 in which 129 people were murdered and which was claimed by the Islamic State (ISIS) organization.
At the start of 2015, 12 people were murdered in an attack on the offices of the satirical magazine Charlie Hebdo attack.
Following the Charlie Hebdo attack, a man linked to ISIS shot and killed a policewoman in a Paris suburb before taking hostages at the Hyper Cacher kosher supermarket the following day, killing four more people.