Arrests following killing of French police officer
What Molins could confirm was that the attacker was well known by French authorities as a potential Islamist radical who lived in a Paris suburb.
While in the slammer, Cheurfi, 39, had also shot and wounded a prison guard after seizing his gun.
A source close to the French investigation said the 35-year-old man being questioned in Antwerp, described as "very dangerous", had been sought by Belgian police as part of a separate probe.
A pump-action shotgun and knives were found in the gunman's auto.
The attack was later claimed by the Islamic State terrorist group (ISIS/ISIL).
Interior Ministry spokesman Pierre-Henry Brandet told BFM television that a man stepped from a auto and opened fire on a police vehicle. Archive reports by French newspaper Le Parisien say that Cheurfi was convicted of attacking a police officer in 2001.
The Paris prosecutor's office said counterterrorism investigators are involved in the probe of Thursday's attack.
"I won't reveal it, because investigations and raids are already under way, in particular to establish whether there is any evidence or not of complicity (in this attack)", he said, adding that more information would be released on Friday.
The man was identified as Youssouf El Osri in a document seen by Reuters.
He had previously also been flagged as an extremist to French authorities, they said.
The home of a 39-year-old man is now being searched, according to a police document obtained by the Associated Press (AP). The Le Parisien newspaper said the address matched that of the owner of the vehicle used in the attack.
The shooting comes two days after the arrest of two men in southern Marseille with weapons and explosives who were suspected of preparing an attack to disrupt the first-round of the presidential election on Sunday.
The Islamic State of Iraq and the Levant (ISIL or ISIS) issued a statement, saying an Islamic State "fighter" had carried the attack.
At 9 p.m., the officers were stopped at a traffic light on the Champs-Elysees - a bustling boulevard popular with tourists and famed for its luxury stores and eateries.
Eric Winkler, 51, a tourist from Boston, told AFP: "It was scary".
"We could, for example, show three faces" instead of two, Frederic Dabi from the Ifop polling institute, told France Info. I have a two year-old girl and I thought I was going to die.