Raids took place at the 39-year-old's Paris suburb home during the night after he killed the policeman and wounded two others in an attack claimed by the Islamic State group.
He was shot dead in return fire while trying to escape, police sources told AFP.
The suspect was arrested in February on suspicion of plotting to kill officers but was released because of lack of evidence.
He had been convicted in 2005 of three counts of attempted murder, with two of these against police officers, sources said.
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The charges dated back to 2001, when he was armed and behind the wheel of a stolen car, which hit another vehicle.
He fled on foot before the driver of the other car and the passenger -- a trainee police officer -- caught up with him. He fired twice, seriously wounding both men in the chest.
He was arrested and placed in custody under a false name.
Two days later he seriously injured an officer who was taking him out of his cell, seizing his weapon and firing several times.
Officials have refused to name the Champs Elysees shooter and are trying to establish if he had accomplices for the attack, which sent people running for their lives on the world-famous street.
'Want to go home'
In the moments after the attack, which came just three days before France's presidential election first round, people hid where they could.
Some took cover in restaurants or shops, others ran into cinemas to get off the strip that is nicknamed "the most beautiful avenue in the world."
"I heard shots and I went to see what it was. I saw two bodies on the ground and people screaming, running everywhere," said Mehdi, a communications consultant. "I was afraid. I left. I didn't even pay the bill!"
The attack's impact on the outcome of one of the most unpredictable election contests in decades is unclear, but far-right leader Marine Le Pen and scandal-hit conservative Francois Fillon immediately cancelled their campaign events on Friday.
The burst of violence and rush of police action left visitors bewildered, and saddened by the new reality of a steady threat of terror attacks in the French capital.
Jihadist-inspired assaults have killed more than 230 people in France since 2015, with many of the victims being people who had gone out for the evening.
Isabel, a 34-year-old Australian tourist, was unable to reach her lodging because of the police lines.
"I just want to go home," she said.
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