Thailand has a grim reputation for its gun culture, business disputes resolved by violence. (file)

A French tourist was gunned down early Wednesday by an off-duty Thai cop after a drunken bar fight in a seedy Bangkok district, police said.

The 41-year-old Parisian was shot dead at a downtown apartment block after an altercation with the police sergeant major who had approached the tourist's Thai girlfriend.

"They were drunk... they started to argue and then had a fist fight but the policeman couldn't fight back," the Chief of Thailand's Immigration Police Surachate Hakpan told news agency AFP.

"The policeman followed him back to his place and shot him twice," he said, adding the victim had been in Thailand for several months.

The officer has been arrested and "will be fired... and prosecuted on a murder charge", Surachate added.

Police are hunting a second suspect seen on CCTV.

Gruesome pictures circulated on Thai media showed the victim lying in a pool of blood in front of a doughnut shop at his apartment block.

Bangkok is one of the world's most visited cities, famed for its food and racy nightlife, much of it around Nana district where the murder took place.

Thailand has a grim reputation for its gun culture, with drunken arguments, business disputes and soured romances frequently resolved by violence.