France's anti-terrorism prosecutors took over the investigation into a fatal knife rampage near Paris on Saturday.
Prosecutors say they have established that the attacker had been radicalised and had carefully planned an act intended to spread terror.
A man identified only as Nathan C stabbed one person to death on Friday in a park in Villejuif, just outside southern Paris, and wounded two others.
The attacker, who had a history of drug and psychiatric problems, was shot dead by police.
"While the troubling psychiatric problems of the individual have indeed been confirmed, the investigations carried out in the last few hours have allowed us to establish a definite radicalisation of the suspect, as well as evidence of planning and preparation carried out before the act," the anti-terrorism prosecutor's department said.
"The steps taken to carry out the murderous act were carefully thought through, and were intended to spread intimidation or terror among the general public."
The department said it was also looking into whether or not Nathan C, who was born in 1997 in Lilas, a northeastern suburb of Paris, had any accomplices. Religious texts including a copy of the Koran were found among his belongings.
The attacker had been to hospital a few months earlier and was undergoing psychiatric treatment. He also had drug problems.
Paris has suffered major attacks by Islamist militants in recent years.
Coordinated bombings and shootings in November 2015 at the Bataclan theatre and other sites around Paris killed 130 people - the deadliest attacks in France since the Second World War.