Investigators looking into the Strasbourg attack are trying to establish whether the main suspect was helped by accomplices while on the run.
Paris prosecutor Remy Heitz, who handles terror cases throughout France, told a news conference that seven people are in police custody, including four members of Cherif Chekatt's family.
The 29-year-old was shot dead last night during a police operation in the Neudorf neighbourhood of the city.
"We want to reconstruct the past 48 hours in order to find out whether he got some support," Mr Heitz said.
Chekatt is suspected of killing three people near Strasbourg's Christmas market on Tuesday night. Mr Heitz added: "A fourth victim is brain dead. Among the 12 other wounded, there is one person in a life-threatening condition and four who remain hospitalised."
After a two-day manhunt, Mr Heitz said, on Thursday evening three officers patrolling in Neudorf spotted a man corresponding to the suspect's description.
He noticed their vehicle and tried unsuccessfully to enter a building. When police officers identified themselves, Chekatt turned around and opened fire.
"A projectile hit the vehicle above the left rear door, two police officers responded, shooting several times, and killed him," Mr Heitz said.
Investigators found a gun, a knife and ammunition on Chekatt's body.
The immediate aftermath of the shootout was caught on camera from across the street, with video footage showing armed officers at the scene and a body slumped in a doorway.
More officers arrive at the scene soon after, followed by crime scene investigators.
The Paris prosecutor's office formally identified the man as Chekatt, a Strasbourg-born man with a history of convictions for various crimes, including robberies. He had been on a watch list of potential extremists.
Witnesses said the gunman shouted "God is great!" in Arabic and sprayed gunfire from a security zone near the Christmas market on Tuesday. Security forces wounded the man but he escaped in a taxi which dropped him off in Neudorf.
More than 700 officers searched for Chekatt, government spokesman Benjamin Griveaux told CNews television.
Chekatt was known to police, but as a common criminal, not a terrorist. He had his first conviction at 13, and had 26 more by the time he died at 29. He served jail time in France, Germany and Switzerland.
- PA
