It is the latest sign of governments cracking down on tax evasion and money laundering after the financial crisis. France is also probing Swiss bank UBS over whether it offered to help clients avoid tax.
An HSBC spokeswoman declined to comment.
The British bank last year agreed to pay a record $1.92 billion in fines to US authorities for allowing itself to be used to launder drug money flowing out of Mexico and for other banking lapses.
The French investigation into the alleged sale of illicit products and tax fraud is based on a list of clients at HSBC's Swiss unit obtained in 2009, the prosecutor's office said.
The list forms part of a batch of data leaked by former HSBC employee Herve Falciani, who is wanted in Switzerland on allegations of stealing data on tens of thousands of bank accounts. Falciani told a Spanish court last week he was a whistleblower fighting corruption.
The French government is fighting to regain credibility on the issue of tax after the dramatic resignation of former budget minister Jerome Cahuzac and his admission earlier this month that he had held a secret bank account in Switzerland.
Government minister Arnaud Montebourg had last week called for the French judiciary to "wake up" on the issue of tax fraud.
A historical bastion of banking secrecy, Switzerland has been under fire for several years for turning a blind eye to the sheltering of taxable income by its banking sector.
UBS, Switzerland's largest bank, paid $780 million in 2009 and handed over thousands of client names to settle US charges that it helped US citizens hide funds.
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