The attacker, who killed a police officer in Paris's Champs-Elysees area, was known for radical Islamist activities by the French security services.
CNN quoted a source as saying that the suspect, who was shot dead by the French Police, was the subject of a "Fiche S" surveillance file and was on the radar of the French domestic security service DGSI.
The Islamic State of Iraq and the Levant (ISIL or ISIS) issued a statement, saying an Islamic State 'fighter' had carried the attack.
The ISIS' claims came via a statement released by the group's media-wing Amaq. The statement said the attacker is a Belgian national.
French president François Hollande said the Champs Élysees attack was "terrorist in nature" and promised "utmost vigilance" by the security services to ensure security around the presidential election.
He has called a defence council meeting for 8am on Friday, The Guardian reports.
Following the shoot out, the Champs-Elysees area was closed and authorities asked the people to avoid the area.
The shooting comes three days before the French general elections.
The anti-terror prosecutors in France have opened investigation into the attack.
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