The attempted robbery of BNP Paribas is the third time this year so-called "termite gangs" have tried to rob a bank by digging a tunnel into the building.
It is not known whether the three incidents are related. A BNP Paribas spokesman was unavailable for immediate comment.
The gang dug into the bank's basement, possibly via the sewage system, but failed to enter the safety deposit room.
They aborted the attempt and started a fire to cover their tracks, which set off alarms and alerted police. Digging equipment, including a pneumatic drill, was found at the scene.
"The individuals left the premises before they could reach the safety deposit room of the bank," Paris police headquarters said in a statement.
Last weekend, a Credit Lyonnais branch in Paris was broken into by tunnel-digging robbers who cracked almost 200 private safes, according to police. A branch of Caisse d'Epargne in a Paris suburb was robbed at New Year in a similar fashion.
French media have compared the cases to the "Spaggiari Affair,” a heist masterminded by Albert Spaggiari more than 30 years ago in Nice.
Then, a gang tunnelled into the vault of a branch of Societe Generale during a public holiday, spent two days and two nights there and made off with about 24 million euros ($32 million) worth of cash and valuables. The heist spawned several books and movies.
