The gunman, who had reportedly held several people hostage, has been arrested and all the hostages have been freed, said the police.
The situation did not appear to have any link to extremist attacks, said police.
Police sources said several post office clients had managed to escape and that the gunman himself had called them. The sources said he was "speaking incoherently" and was heavily armed with grenades and Kalashnikovs.
The area around the post office in Colombes, a city northwest of Paris, had been cordoned off, with a helicopter flying overhead and elite security forces on the ground.
The French capital is still jittery after a series of attacks last week by Islamist gunmen left 17 people dead.