A drunk man on Sunday was killed by French police outside Paris after threatening officers and shouting "Allahu akbar," an Arabic expression often shouted by Islamist attackers.

According to preliminary information, the man brandished what turned out to be a dummy gun, a source close to the case said. He was "very drunk," the source said.

At around 6.00 am (0500 GMT), police were called to an incident which saw an armed man bang on a door in Villeneuve-Saint-Georges in the southeastern suburbs of Paris, one of the police sources said.

The man threatened the police "by pointing a handgun and shouting 'Allahu akbar'," a Muslim expression of faith meaning "God is greatest," the source added.

A police officer then drew his weapon and shot the man, who died despite the intervention of the emergency services, the source said.

According to another police source, the officer fired his weapon three times, and the man was hit once. The entire incident was captured by the police body camera.

The man, aged 30, committed an "apology for terrorism" in 2019, according to police sources.

The case has been referred to the police's IGPN internal affairs department, which is a standard procedure.

The police officer who shot the man tested negative for drugs and alcohol. (AFP)