The attacker is believed to have deliberately targeted the officers, according to reports.
They were attacked on the Champs-Elysees - one of the French capital's main shopping streets.
Security has been tight in the country, coming just days before the first round in France's presidential election on Sunday.
At least two attackers are reported to be involved and authorities are warning people to avoid the area.
An eyewitness told Reuters a man got out of a car and began shooting "with a Kalashnikov".
Security has been tight in the country, coming just days before France's presidential election on Sunday.
Police say the officer who was killed was in a car which had been stopped at a red light.
But other reports from French media say only two shots were fired in the incident near the Marks and Spencer store and one of the attackers could be still at large.
An interior ministry spokesman said it was too early to say what the motive was for the attack.
It is not known whether it was terror-related.
But the shooting could have been an attempt at an armed robbery, according to police sources.
Many police vehicles can be seen on the famous avenue.
A witness identified only as Ines told French television station BFM that she heard a shooting, saw a man's body on the ground and the area was quickly evacuated by police.
Who'd be a policeman's wife?
And who could forget this sickening video of the death cult of Muhammad in action previously in Paris.