The officer has been charged with homicide and remains in custody.
In their outline of events after questioning eyewitnesses and reviewing CCTV footage, prosecutors say the teenage driver had already ignored a police demand to stop, when officers caught up with the car and drew their weapons.
Meanwhile an account has been posted online by one of the passengers, which French media say they have verified but the BBC has not.
In this account the passenger, also a teenager, says the officers hit Nahel M with the butts of their guns three times, causing him to take his foot off the brake of the car.
Prosecutors are due to talk to this witness on Monday.
Here's what we know.
What prosecutors say happened
Around 08:00 on Tuesday, two policemen on motorcycles spotted a Mercedes with a Polish number plate driving fast in a bus lane, Nanterre prosecutor Pascal Prache told journalists.
Turning on their siren, the officers caught up with the car at a traffic light. Three young men were inside.
The officers told the driver to stop but the vehicle pulled away, ignoring the red light. The officers gave chase and notified their unit by radio.
At 08:16, the Mercedes stopped in heavy traffic. Both officers got off their motorcycles, drew their weapons and approached the car.
They later told prosecutors that they pointed their guns at the driver to "deter him from driving away again".
They asked the driver to turn off the ignition, but the car moved forward. One of the officers fired, fatally wounding the young man in the chest.
After the car ran into a roadside barrier, one of the passengers was arrested and the other fled on foot.
The witness account
The passenger says the three friends were driving around Nanterre when the car strayed into the bus lane and was chased by two policemen on motorcycles.
After Nahel stopped the car, the young man says in his video and in an interview with Le Parisien newspaper, one of the officers hit the teenage driver with the butt of his gun.
He alleges that the second policeman also struck Nahel before the first officer again hit him.
He told Le Parisien that the blows left Nahel M "a little stunned".
The third blow, according to this account, caused Nahel to take his foot off the brake and the vehicle to move forward. After the officer fired, Nahel M slumped forward and his foot pressed on the accelerator, the passenger said.
When the car came a standstill, the passenger said, he decided to flee because he was afraid he would be shot too.
Car was a rental vehicle
Questions have been asked about the car, a Mercedes A class AMG. Officials describe it as a rented vehicle.
The passenger who fled said that someone had lent it to the three youths, without giving any details.
According to the French motoring website Autoplus, German sportscars with Polish number plates can be hired for €300-3,000 (£260-2,600) a day.
This type of short rental is popular with young men in French housing estates, Autoplus says.
Nahel M did not have a criminal record but was known to police.
He had previously been cited for driving without a licence - he was too young to have one - and for refusing to comply with an order to stop.
He was due to appear before a juvenile court in September.