Le Monde said France's DGSE was interested in finding out who was speaking to whom than in combing through the content of private communications. It said the DGSE stored such metadata in the basement of its Paris headquarters.
The activities described are similar to those carried out by the U.S. National Security Agency, as described in documents leaked by former NSA contractor Edward Snowden.
Le Monde's report also comes amid allegations by German magazine Der Spiegel that Washington spies on European citizens and embassies.
The European Parliament on Thursday called on the U.S. to provide full disclosure of any spying activities, and set up an inquiry to look into the allegations.