After killing the officer and injuring his colleagues just a few hundred metres from the Arc de Triomphe, the gunman was shot dead in return fire while trying to flee on foot, police sources told AFP.
A statement from extremist group published by its propaganda agency Amaq said the attacker was "one of their fighters."
The killer, identified as a 39-year-old French man, was known to anti-terror police, sources told AFP, and raids took place at his address in a suburb to the east of Paris.
He 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 impact on the outcome of the French election is unclear -- Sunday is the poll's first round -- but far-right leader Marine Le Pen, her centrist rival Emmanuel Macron, and scandal-hit conservative Francois Fillon cancelled campaign events planned for Friday.
Up until now, surveys showed voters more concerned about unemployment and their spending power than terrorism or security, though analysts warned this would change in the event of violence.
The shooting comes two days after the arrest of two men in southern Marseille with weapons and explosives who were suspected of preparing an attack to disrupt the campaign.
French President Francois Hollande promised "absolute vigilance, particularly with regard to the electoral process" and paid tribute to the police.
Hollande, who said he was convinced the shooting was a "terrorist act", cancelled a trip to Bretagne and will chair a security cabinet meeting Friday.
-AFPÂ
