Le Monde Diplomatique said the base is located near Kibbutz Urim in the Negev, not far from the city of Beersheba.
Israeli daily newspapers published details of the report Sunday, noting the location of the base had been kept secret prior to the French report.
The magazine also had photographic images showing the location of the base -- some downloaded by Google Earth and others taken from the roadside.
The base has 30 antennas and satellite dishes capable of eavesdropping on telephone calls and accessing the e-mail of "governments, international organizations, foreign companies, political groups and individuals in the Middle East and Europe, " the Haaretz newspaper said.
The base is home to the Israel Army's intelligence unit 8200.
The French magazine said one of the base's main purposes is to listen to transmissions from ships in the Mediterranean. It also has the capability to tap underwater communication cables, mostly in the Mediterranean, connecting Israel with Europe.
Haaretz said the author of the article, Nick Hager, is a New Zealand investigative reporter specializing in intelligence and technology related stories involving signals intelligence.
Haaretz said some of the military unit's successes include the interception of a telephone call between Egyptian president Gamal Abdel Nasser and King Hussein of Jordan during the first day of the Six-Day War, and the interception of a call between Yasser Arafat and the terrorist group that hijacked the Achille Lauro cruise ship in the Mediterranean in 1985.