One person was killed and two were injured in a knife attack near Paris, with the attacker shot dead by police.
A man, 22, stabbed passers-by in a park in Villejuif, about 8km (5 miles) south of the French capital, on Friday.
He was later identified by prosecutors as Nathan C, a 22-year-old with a history of mental illness for which he had been admitted to hospital.
According to French media, witnesses heard him say that he was "out of medication".
Prosecutors said that some religious items were later found in his bag, but that there was "no evidence at this stage suggesting he was radicalised".
The attack took place at about 14:00 local time (13:00 GMT) at Hautes-Bruyères park, and the targets appeared to have been chosen at random.
In a statement posted on Twitter, French President Emmanuel Macron paid tribute to the victims.
"I extend my support to the victims of the attack, their families and the police," he said. "We resolutely pursue the fight against indiscriminate violence and our fight for the security of all French people."
The mayor of Villejuif, Franck Le Bohellec, said the deceased victim was a 56-year-old man who was out walking in the park with his wife at the time of the attack.
He died trying to protect her, the mayor said. She was seriously injured.
France's Deputy Interior Minister Laurent Nuñez, who later visited the scene, praised the police response, calling it "extremely courageous".