President Emmanuel Macron described Friday's shooting in Trappes, near Paris, as a terrorist and racist attack which marked a turning point in the history of France.
Macron said the victims of the Trappes gunman were targeted solely due to their religion and the colour of their skin.
"What happened today marks a turning point for the Republic and our country. What happened today was a terrorist and racist attack," Macron told reporters.
Interior Minister Laurent Nunez earlier told reporters the shooting was "clearly a terrorist crime".
"The investigations are ongoing, but it is clearly a terrorist crime. It is an extremely serious act," Nunez told reporters from the Yvelines district west of Paris where the attack took place.
Officials said the 39-year-old suspect, who has not been named, drove through the town of Trappes, where he fired an automatic weapon at a petrol station, a medical centre and a children's playground.
Broadcaster BFM said the wounded girl had been hit eight times and was in a serious condition.
"(It was) objectively a racist attack, probably Islamophobic," said Ali Rabeh, the mayor of Trappes, whose parents came from Morocco.
"The people targeted today could just as easily have been my mother, my brothers or my sisters-in-law."
Police managed to arrest the man before he could injure anyone else. Video images showed his car riddled with bullets.
The shooting comes at a moment of particular tension in France, after nationwide protests turned violent last Saturday and before further demonstrations this coming weekend.
Some far-right politicians have blamed immigration for the wave of looting and vandalism that battered a number of French cities on October 17.
Rabeh, who is a left-wing politician, called for a collective condemnation of rhetoric that "ideologically arms those capable of carrying out such acts".
The anti-terrorism prosecutor's office, known as PNAT, said its investigation included looking at whether the shooting was racially or religiously motivated.
PNAT can take over any criminal investigation it believes meets the criteria for terrorism, including violence inspired by far-right ideas. Terrorism sentences are tougher, and counter-terrorism forces have greater investigative powers.
Nicolas Dainville, the mayor of nearby La Verriere, said the suspect lived in the town of Plaisir, which is also in Yvelines, and was "of a European type".
Rabeh said two of the victims were of African and North African origin, respectively, and did not provide details about the backgrounds of the other victims.
