* Settles long-running tax evasion investigation
* First settlement under new French legal framework (Adds detail, background)
ZURICH, Nov 14 (Reuters) - HSBC Holdings has agreed to pay 300 million euros ($353 million) to settle a long-running investigation into tax evasion by French citizens via its private bank in Switzerland, the lender said on Tuesday.
The agreement is a first under a French system introduced in 2016 to allow companies to settle without any finding of guilt, HSBC said in a statement, adding the fine had been fully provisioned.
"The investigation regarding HSBC Holdings has been dismissed," HSBC said in its statement.
Governments around the world are working to clamp down on tax evasion, given public anger at the perception that the richest members of society may not be paying their full dues.
The French financial prosecutor's office also confirmed the settlement ends proceedings against HSBC, provided that HSBC makes the payment.
It added, however, that two unnamed former directors of HSBC's Swiss private bank remained subject to possible legal action.
HSBC's Swiss private bank was plunged into turmoil in 2008 when Herve Falciani, a former IT employee, leaked client data that has spawned investigations in several countries.
Falciani, a French citizen, has said he is a whistleblower trying to help governments to track down citizens who used Swiss accounts to evade tax. In 2015 a Swiss court sentenced him in absentia to five years in prison for industrial espionage.
"HSBC has publicly acknowledged historical control weaknesses at the Swiss private bank on a number of occasions and has taken firm steps to address them," the bank said.
The French investigation found that several French taxpayers had not declared to tax authorities assets held in the books of the Swiss private bank, which provided French clients with services used to conceal assets.
Swiss bank UBS has not agreed on a settlement in a similar case in France and now faces trial after a long-running investigation into allegations it helped wealthy clients to avoid taxes. ($1 = 0.8508 euros) (Reporting by Michael Shields; Additional reporting by Sudip Kar-Gupta; Editing by David Goodman)