Emmanuel Macron's statements come after protests over a killing that swept through the Paris region during the night.
Nahel, 17, was shot in his car after failing to stop when ordered to do so.
A video circulating on social media shows an officer pointing his gun at the car's driver before a gunshot is heard and the car crashes to a halt.
Despite emergency services' efforts, the young man died from a bullet wound to his chest.
The officer accused of fatally shooting him has been arrested, as the video appeared to contradict his initial claims that he fired his gun because he felt his life was in danger.
A series of protests followed the shooting on Tuesday evening in Nanterre, the western Parisian suburb where the young man was killed. 31 people were arrested in the aftermath of the unrest.
Nahel is the second person to be killed this year in France in a police shooting during a traffic stop. Last year, 13 people died in this way.
According to French media, the police initially suggested that the teenager drove his car towards them with the intention of harming them.
However, footage that was posted online and verified by the French news agency tells a different story.
Two officers appear in the car, with one pointing his weapon at the driver through the window and appearing to fire at close range as he tries to drive away.
The agency also reported that a person can be heard in the video saying, "Shoot him in the head" - but it is unclear who said it.
There were two other individuals in the car at the time of the shooting. One of them fled while the other, also a minor, was apprehended by the police and detained.
The incident sparked anger and unrest overnight, with cars and trash cans set on fire and bus shelters destroyed. Fireworks were also launched near the police station. Riot police used tear gas to disperse the protesters, some of whom set up barricades throughout the night.
President Macron told reporters in Marseille, "Nothing justifies the death of a young man," calling for "calm to ensure justice is served.
I would like to express the feelings of the entire nation for what happened and the death of young Nahel, and to convey our solidarity and the nation's emotions to his family.
The President said, "We have a teenager who was killed. It is an inexplicable and unforgivable act," adding that the case was immediately referred to the courts where he hopes "justice will do its job quickly.
The President's statements aim to calm the volatile atmosphere in Nanterre, near the La Defense business district, and other suburbs of Paris where Nahel's death has stirred strong emotions.
Protests and Unrest Follow Fatal Shooting of Teenager by French Police
In response to concerns about the possibility of further rioting on Tuesday evening, the government announced that there would be strong police reinforcements on the streets.
The shooting in Nanterre is set to be one of those defining moments that characterizes the troubled relationship between the police and angry residents in urban or suburban areas.
The government can see this like anyone else, which is why it will tread very cautiously in the coming days. Gerald Darmanin, the Interior Minister, set the tone when he said that the police's actions - in his view - were unacceptable.
The danger is that Tuesday's rioting could spill over into the coming nights. The hot weather, long evenings, and end of the school term can easily combine with a sense of righteous anger to push more young people onto the streets.
The long nights of rioting in the suburbs in 2005 have not been forgotten.
One initiative that could be considered is a review of the rules of engagement for police officers at checkpoints.
Second Fatal Incident in France This Year Involving Police and Traffic Stops
No one disputes that refusing to stop at a traffic checkpoint is a serious offense and happens frequently. But on 13 occasions last year, car passengers were killed in such situations by French police gunfire. This strongly suggests that something is wrong.
In a video posted on TikTok, Nahel's mother, Monia, urged people to join her in a march for her son.
Come on, I beg you," she said. "We will all be there.
Footballer Kylian Mbappe Expresses Solidarity with Family of Slain Teenager
French footballer Kylian Mbappe tweeted, "I am hurting for France. Unacceptable situation. All my thoughts go to Nahel's family and loved ones, this little angel gone too soon."
Authorities have opened separate investigations into the teenager's death - one into a possible killing by a public official, the other into the driver's alleged failure to stop his car and attempt to kill a police officer.
Paris police chief Laurent Nunez told French TV station BFMTV that the officer's actions "raise questions," although he suggested that the officer may have felt threatened.
The lawyer for the family of 17-year-old Yassine Bouzrou confirmed that this was an unlawful defense, telling the same channel that the video "clearly shows a policeman killing a young man in cold blood.
He added that the family had filed a complaint against the police for "lying" - after initially claiming that the car had tried to run over the police officers.
Tuesday's killing is the second fatal incident in France during this year's traffic stops.
Two weeks ago, a 19-year-old driver was shot dead by police in the town of Angouleme in western France after he hit an officer in the legs during a traffic stop.