The suspect who placed the device was accompanied by a second person, who appeared to be taking photos and videos with a mobile phone but fled when police arrived.
The device contained five litres of liquid believed to be fuel and an ignition system, a source close to the investigation said.
Police said the suspect arrested early on Saturday outside the bank had told them he was a minor and from Senegal. They were working to verify his identity.
According to a police source, the first suspect said he had been recruited through the Snapchat app to carry out a bombing in exchange for €600 ($1203).
The PNAT told AFP on Saturday it had launched a probe into “attempted damage by fire or other dangerous means”.
The incident came after more than a month of US and Israeli bombardment of Iran.
The war has escalated into a regional conflagration, with Iran retaliating by attacking Gulf states, sending energy markets into a tailspin and threatening the world economy.
The French Government and security services have said that while they do not believe France itself is a target, US and Israeli interests on its soil might potentially be singled out.
Nunez said he did not know who was behind the incident but added that it might have been “proxies” linked to Iran.
- Agence France-Presse