A driver rammed his vehicle into a police van in the heart of Paris on Monday...hours after a van ploughed into worshippers near a mosque in north London.
The family members were taken into custody after being questioned by police at the family home, according to judicial sources.
Sources close to the probe said he had been on France's security watchlist since 2015 over ties to "the radical Islamist movement".
The 31-year-old suspect, believed to be a known terror sympathiser, died in the apparent terror attack. The man had a gun permit, which was granted shortly before he was flagged with authorities. "It's a hard decision".
Guns - including a Kalashnikov - as well as bottles containing gasoline were found in the auto, according to French media.
But French Interior Minister Gerard Collomb called it an "attempted attack" on security forces, and France's anti-terrorism prosecutor has opened an investigation.
Collomb also said there were weapons and explosives inside of the auto.
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A Kalashnikov rile, handguns and gas bottles were found in the auto, sources told AFP. The auto burst into flames on impact.
A vehicle careered towards a French Gendarme van on Paris' famous Champs Elysees, and exploded on impact.
Earlier this month an Algerian man attacked a policeman with a hammer outside Notre Dame cathedral, another key tourist draw, while troops shot dead a man at the capital's Orly airport in March after he attacked a soldier on patrol. "No one place is safe in the world".
France also has a history of deadly vehicle attacks: In July 2016, an Islamic State-inspired assailant plowed through crowds gathered to celebrate Bastille Day, the national holiday, on a seaside promenade in Nice, killing 86. He wants France's government to extend the state of emergency a few more months to November 1.
"This shows again that the level of terrorist threat is still extremely high in France", the minister told reporters at the scene.
"We need to find legal instruments that at once guarantee that we continue to live in a Fifth Republic which safeguards freedoms and ensure the security of French people", Philippe said.
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