The man, aged 24, attempted to rob a BNP Paribas in the city's upmarket 17th arrondissement at around 9 am on Friday morning.
He was shot by police during his arrest which left him with wounds “in the thigh and perhaps in the chest,” according to French press reports.
He has since been hospitalised.
The video below shows police officers with the man after he was injured.
The incident took place at the BNP Paribas branch located at 24 avenue de la Grande Armee (see map below) just 400 metres from the Arc de Triomphe monument, one of the city's biggest tourist attractions which commemorates the country's military victories and war dead.
A 24-year-old man burst into the bank on Avenue de la Grande Armee shortly after it opened. The alarm was raised and the police were waiting for the man when he came out brandishing a gun.
The police said he was a known criminal, with a history of armed robbery.
Paris has been the scene of several spectacular robberies in recent years, mostly involving jewels.
Map shows where the incident took place. Google maps
Indeed, this incident comes just one month after a gang of five robbers armed with hatchets launched a spectacular raid on the world famous Ritz hotel in Paris, making off with an estimated four million euros worth of jewels.