France's foreign intelligence service intercepts computer and telephone data on a vast scale like the Prism programme in the United States, newspaper Le Monde says.
The French paper says the data is stored on a supercomputer at the headquarters of the DGSE intelligence service.
It says connections inside France and between France and other countries are all monitored. The data is reportedly stored on three basement floors of the DGSE building in Paris.
Le Monde said the operation is designed to uncover terrorist cells. But the scale means that "anyone can be spied on, any time".
The BBC says French officials have not yet commented on the report.
The scale of surveillance by the National Security Agency in the United States emerged from leaked classified intelligence documents.
The BBC says the GCHQ in Britain is reported to run a similarly vast data collection operation, co-operating closely with the NSA.