Interior Minister Manuel Valls described the revelations in Le Monde newspaper as "shocking", in an interview with French radio Europe 1.
The spy agency taped 70.3 million phone calls in France over a 30-day period between December 10 and January 8 this year, Le Monde reported in its online version, citing documents from former US security contractor Edward Snowden.
According to the paper, the NSA automatically picked up communications from certain phone numbers in France and recorded text messages under a programme code-named "US-985D."
US authorities declined comment to the French daily on the "classified" documents.
More From This Section
The Le Monde article followed similar revelations by German weekly Der Spiegel that US agents had hacked into the email account of former Mexican president Felipe Calderon.
Mexican authorities have said they will be seeking answers from US officials "as soon as possible" following the allegations.
Snowden, who has taken refuge in Russia, is wanted in the United States for espionage and other charges after leaking details of the NSA's worldwide snooping activities.