A police document obtained by the Associated Press (AP) identifies the address searched in the eastern Paris suburb of Chelles as the family home of Karim Cheurfi, a 39-year-old with a police record.
The Frenchman was convicted of attempted murder after shooting at two police officers in 2001 when they tried to stop his stolen car.
While serving a 10-year sentence, he also shot and wounded a prison officer after grabbing his gun.
Released in 2015 on probation after another two-year sentence for lesser offences, he was detained again in February this year after threatening to kill police.
However, Cheurfi was released due to lack of evidence, said two officials who spoke to AP anonymously.
He had previously also been flagged as an extremist to French authorities, said the police sources.
Police tape surrounded the quiet, middle-class Chelles neighbourhood as residents expressed dismay at the searches.
A neighbour said: “I think everyone here is in shock. It’s clear that we are in shock. And that we’ve got to this point is very serious. Especially because this doesn’t seem to resemble anyone from Chelles.
“I don’t know anyone here who could just lose it and do this kind of thing.
“I never noticed anything abnormal about the guy. And this was a guy who was very closed off and was not someone who looked for problems.”
The details emerged as police detained three relatives of the suspected gunman and raided properties across the capital.
It is not certain whether the attack, in which a police officer was shot dead and two seriously injured, was terror-related, but French President Francois Hollande described it as “terrorist in nature”.
The gunman was shot dead at the scene and a pump-action shotgun and knives were found in his car.
An anti-terror investigation is under way into the incident at the heart of the French capital, which Islamic State has said it carried out.
The extremist group named the attacker as Abu Yusuf al Beljiki and suggested he was a Belgian.
Interior ministry spokesman Pierre-Henry Brandet said it was too early to say what the motive for the attack was, but that it was clear the police officers had been deliberately targeted.
Security expert Major General Chip Chapman told Sky News: “French security agencies know 2,000 dangerous or potentially dangerous terrorists in France. But you only have resources to follow so many.”
The incident follows two recent attacks on soldiers providing security at prominent locations around Paris – one at the Louvre museum in February and one at Orly airport in March.