Emmanuel Macron has described the fatal shooting in a Paris suburb as a terrorist and racist attack which "marked a turning point" in the history of France.
The French president said the victims of the attack on Friday were targeted due to their religion and skin colour.
"What happened today is, I am telling you, a turning point, because it is the first time we have had a terrorist act that was planned to kill our compatriots, our children, based on the colour of their skin or their religion," Mr Macron said.
"There is no place for this in France."
A suspect has been arrested after one person was killed and several others wounded, including a 12-year-old girl, who was seriously injured.
The anti-terrorism prosecutor said on Friday evening the 39-year-old suspect had been identified as Kevin T. His surname was not given, as is common practice in such criminal inquiries in France.
The prosecutor added a Sten gun, a type of submachine gun developed during World War Two, and a tear gas grenade were found in the suspect's car.
The shootings, which saw the attacker fire from a vehicle, happened at three separate locations in the towns of Trappes and La Verriere, said interior minister Laurent Nunez.
They are about 15 miles southwest of central Paris, in the Yvelines department.
Investigations by the anti-terrorism prosecutor's body, which is leading the case, were still ongoing.
Mr Macron said the gunman had deliberately chosen not to fire upon some people due to their skin colour and appearance.
Ali Rabeh, the mayor of Trappes, told BFMTV a man had fired shots on a road between Trappes and La Verriere.
He said he "appeared to be firing at random and seemed intent on carrying out a massacre" and it was a "miracle" there were not more victims.
Mr Rabeh said the person killed was of African origin, while another of the wounded was of North African origin.
He said a playground was among the locations attacked, with BFMTV reporting the 12-year-old girl had been hit eight times.
Police have not yet commented on the identity or ages of the victims.
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The attack happened as France braces for more protests on Saturday over the high cost of living and the state of schools.
The government is deploying a much larger security presence to try to prevent a repeat of last week's widespread unrest and violence.
Mr Nunez said around 70,000 security personnel would be on duty. Major museums, such as the Louvre, will also stay closed.
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