Swiss banking giant UBS said in July that the Swiss authorities had asked it to provide client information following a French request for international administrative assistance in May.
The demand concerns former and current clients living in France, based on data from 2006 to 2008.
Le Parisien on Monday published extracts from a letter dated May 11th from French tax authorities. It said that France was chasing the names of the owners of "more than 45,161 different account numbers."
"The assets of those listed totaled more than 11 billion Swiss francs ($11 billion), which could represent a several billion dollar shortfall for the French treasury," according to the letter written by French tax
authorities, the report said.
According to the report, French authorities have already identified 4,782 accounts and are seeking to find the owners of an additional 40,379 accounts.
France opened a probe into UBS after former employees blew the whistle over the bank's alleged system of setting up dual accounts to hide the movement of capital into Switzerland between 2004 and 2012.
UBS denies the accusations, arguing that its involvement in such financial operations has not been proven.
Meanwhile, the documents Germany handed to French judges last year allowed them to evaluate the assets of French clients held by the bank in 2008 at nearly €12 billion ($13.5 billion), according to a source close to the investigation.
However not all involved tax evasion.
UBS has been embroiled in a whole series of similar cases, most notably in the United States where the authorities said the bank used Switzerland's banking secrecy laws to help rich clients avoid the taxman.