"They made the most of their time to break open the deposit boxes of several of the bank's users. Once they had committed their crime, they left the imprisoned staff who were able to free themselves and alert the police," said Sid.
Two people were lightly wounded during the hold-up, according to the Paris fire brigade. The bank, in the upmarket 8th arrondissement, caters to wealthy clients.
Paris' crime squad has launched an investigation.
On Tuesday afternoon, numerous police vans were parked outside the bank including a mobile forensic unit and the area was cordoned off.
"We heard and saw nothing," Pierre, a vendor of a shop opposite the bank, told AFP. "Only when the police turned up did we find out what had happened. We were told to remain inside the shop. It lasted for two hours then we were able to open up again."
There have been a number of spectacular robberies in Paris in recent years, several of them on jewellery stores.
The highest profile heist was when five thieves dressed as police officers bound, gagged and robbed American reality TV star Kim Kardashian West of around $10 million of jewels at gunpoint in her rented Paris flat in October 2016.
French police arrested 10 people in January 2017 in their hunt for the gang of robbers.
Her bodyguard was last October sued for €6.1m by the celebrity's insurer for "negligently" protecting her private flat.
In February last year, an armed man tried to attack a BNP bank branch near the Arc de Triomphe and was wounded by police during his arrest.
In 2017, a luxury watchmakers' boutique on the Champs-Elysées was also targeted by two men who made off with "hundreds of thousands" of euros-worth of jewellery.
This article originally appeared on the Daily Telegraph.
