The knife-wielding assailant stabbed at least four passers-by, killing one of them, in the busy Opera district of central Paris on Saturday night.
The 21-year old attacker — who was not identified by name — was shot by police as he rushed at the officers, shouting, “I will kill you, I will kill you!”
The assault was later claimed by the Takfiri Daesh terrorist group.
The assailant’s father and mother are being held for questioning by police, a judicial source said.
Another source said the attacker was not previously known to police and had no criminal records.
But prosecutors said the assailant had been categorized in France as “fiche S,” an indication used by law enforcement officials to flag people who may be a threat to national security.
Shortly after the attack, President Emmanuel Macron said France “will not yield an inch to the enemies of freedom,” and praised police officers for “neutralizing the terrorist.”
Interior Minister Gerard Collomb also announced that those injured in the attack were out of danger.
France is still on high alert after a string of attacks claimed the lives of more than 245 people around the country over the past three years.
On January 7, 2015, two Takfiri militants attacked the office of the Charlie Hebdo magazine, killing 12 people.
A day after the magazine attack, another militant killed a policewoman. Still a day later, the same assailant took people hostage at the HyperCacher supermarket and killed four of them before being shot dead by police.
Daesh also launched a series of violent attacks in November 2015, targeting cafes and a concert hall in Paris. A total of 130 people lost their lives in those attacks.
In July 2016, a truck driver deliberately plowed through a Bastille Day crowd in Nice, killing 84 people and wounding 200 others. An 85th victim of the attack — which was also claimed by Daesh — died later in hospital.
France lifted a state of emergency states put in place just after the Paris attacks in November 2015, but soldiers continue to patrol major tourist sites and transport hubs under an anti-terror mission.