Whistleblower website WikiLeaks reports the NSA spied on Francois Hollande, Nicolas Sarkozy and Jacques Chirac between 2006 and 2012.
President Francois Hollande called an emergency meeting and said France would “not tolerate” acts that threaten its security.
The US said it would not comment on “specific intelligence allegations”.
Ned Price, a spokesman for the US National Security Council, added that the US was “not targeting and will not target the communications of Mr. Hollande”.
The NSA has previously been accused of spying on German Chancellor Angela Merkel and on Brazilian and Mexican leaders.
French Foreign Minister Laurent Fabius has summoned US Ambassador Jane Hartley to discuss the latest claims, French officials said.
Jane Hartley is expected to visit the foreign ministry in Paris on June 24.
A statement from the French presidency said the US must respect a promise not to spy on French leaders. The statement came after an emergency meeting of security chiefs in Paris.
A senior French intelligence official is meanwhile expected to visit Washington to discuss the spying claims.
WikiLeaks began publishing the files on June 23, under the heading “Espionnage Elysee” – a reference to the French presidential palace.
It said the secret files “derive from directly targeted NSA surveillance of the communications” of the three French presidents as well as French ministers and the ambassador to the US.
The WikiLeaks files have now been published by France’s Liberation newspaper and the Mediapart investigative website.
One of the files, dated 2012, is about Francois Hollande discussing Greece’s possible exit from the eurozone. Another one – from 2011 – alleges that Nicolas Sarkozy was determined to resume peace talks between Israel and the Palestinians, possibly without US involvement.
A file dated 2010 suggests that French officials were aware that the US was spying upon them and intended to complain about it.
According to the summary of an intercepted exchange, the French envoy to Washington and Nicolas Sarkozy’s diplomatic adviser discussed Sarkozy’s plan to express his “frustration” over US unwillingness to sign a “bilateral intelligence co-operation agreement”.
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