"The reported spying creates a discomfort, because there is a breach of trust. But, it is absolutely important and vital for both countries to maintain their partnership, given that there are many sensitive issues such as Ukraine, operations in Iraq which remained unsolved," Ulysse Gosset, journalist specialized in foreign politics told news channel BFMTV.
To Edwy Plenel, French political journalist and editor-in-chief of news website Mediapart, which reported WikiLeaks revelations, it is "a real problem of loyalty in international relations between allies".
French Foreign Minister Laurent Fabius summoned U.S. ambassador Jane Hartley for an explanation on "Espionage Elysee" of WikiLeaks.
Urging a strong answer to United States' spying on Paris, critics from the right and left wing parties called for retaliation. But, according to the ruling Socialists, a diplomatic spat is not in the air.
"In the face of threats that we face and given the historic ties linking us, we have to keep a perspective. We're not going to break diplomatic ties," said Stephane Le Foll, the government's spokesman after a weekly cabinet meeting.
Following the allegations of U.S. spying on French interests, which had emerged for the second time in two years, Le Foll announced a senior French intelligence official would be dispatched to the United States "to verify this spying has finished."
"Between allies, this is unacceptable and incomprehensible. France does not spy on its allies," he stressed.
A statement from the U.S. National Security Council said it was not targeting and would not target Hollande's communications, but did confirm that spying had taken place in the past.
However, after a phone discussion between French president Francois Hollande and his American counterpart Barack Obama, Elysee seemed much calmer but hazy.
"President Obama reiterated unequivocally his firm commitment to end the practices that were allowed to happen in the past and that were unacceptable among allies," said the statement of the Elysee, without clarifying France's reaction after the phone discussion.
But "the French intelligence officials will travel soon to Washington to deepen the cooperation", according to the statement.
In 2013, Hollande and German Chancellor Angela Merkel set "a code of conduct" for Washington that imposes new rules on spying following reports published that the United States tapped German leader's mobile phone and snooped on millions of French telephone call.
France is a close ally of the United States, and plays a key role in a number of U.S.-associated international institutions, including the Group of 7 and NATO.