The French newspaper Le Monde said on Thursday the DGSE intercepted signals from computers and telephones in France, and between France and other countries, although not the content of phone calls, to create a map of "who is talking to whom". It said the activity was illegal.
"All of our communications are spied on," wrote Le Monde, which based its report on unnamed intelligence sources as well as remarks made publicly by intelligence officials.
"Emails, text messages, telephone records, access to Facebook and Twitter are then stored for years," it said.
The activities described are similar to those carried out by the US National Security Agency, as described in documents leaked by former NSA contractor Edward Snowden.
The documents revealed that the NSA has access to vast amounts of Internet data such as emails, chat rooms and video from large companies such as Facebook and Google, under a program known as Prism.
They also showed that the US government had gathered so-called metadata - such as the time, duration and numbers called - on all telephone calls carried by service providers such as Verizon.