Britain's Financial Secretary to the Treasury David Gauke said in parliament this week that France had provided leaked information on accounts at the British bank "under very strict conditions".
In response, French Finance Minister Michel Sapin told newspaper Le Monde he "did not understand" Gauke's remarks.
"The HSBC data were sent to them in 2010 under our bilateral conventions," Sapin said in the interview, adding: "If the British tax authorities wanted to open a court case, they most certainly could. Then it's a matter of judicial cooperation."
France has had access to leaked HSBC client data since 2008, according to the International Consortium of Investigative Journalists (ICIJ), which coordinated the release of details.
HSBC has admitted failings in compliance and controls at its Swiss bank after the ICIJ organised the simultaneous publication of client names and details by several media outlets.
Gauke said British tax authorities were seeking information from the ICIJ as the data it had received from France was restricted in use.
"HMRC received the HSBC data under very strict conditions that limited the department's use of it to pursuing offshore tax evasion and prevented HMRC from sharing the data with other law enforcement authorities," he said in parliament on Monday.
"Under these restrictions, HMRC has not been able to seek prosecution for other potential offences such as money laundering," he added.
Gauke said the French had that same day confirmed they would help the British authorities to "exploit the data to the fullest".
(Reporting by Leigh Thomas, Additional reporting by Tom Bergin in London; Editing by Laurence Frost and Gareth Jones)