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.
The charges dated back to 2001, when he was armed and behind the wheel of a stolen car, which hit another vehicle.
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.
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