The tax evasion revealed in the documents "is likely to concern French taxpayers," the French financial prosecutors' office said as it announced it was opening a preliminary investigation into money laundering and tax fraud.
French President Francois Hollande had earlier promised that the revelations would lead to "legal proceedings" in France.
"It's good news that we are aware of these revelations because it will bring in tax revenue from those who have defrauded," Hollande said, thanking the whistleblowers for revealing the information from Panamanian law firm Mossack Fonseca.
Spanish state prosecutors also opened a money laundering probe, a judicial source said.
The scandal erupted yesterday when media groups made public a year-long worldwide investigation into a trove of 11.5 million documents that exposed a tangle of offshore financial dealings.
The Kremlin furiously claimed it was the target of a plot to destabilise Russia after documents relating to President Vladimir Putin's close associates were made public.