Speaking on TF1, the anti-secrecy campaigner urged France to go further than Germany: by launching a "parliamentary inquiry" into the foreign surveillance activities and refering "the matter to the prosecutor-general for prosecution".
German prosecutors had carried out a probe into alleged tapping on Chancellor Angela Merkel's phone, but later dropped the investigation due to a lack of hard evidence.
Assange also said other important revelations were coming.
"I think from a policy perspective what is to come is much more significant than what we have published so far," he said.
"But now the question really for (President Francois) Hollande and the French leadership is what are the opportunities in their response to address this situation."
France expressed anger earlier Wednesday after leaked documents labelled "top secret" appeared to reveal US spying on Hollande and his two predecessors, Nicolas Sarkozy and Jacques Chirac, between 2006 and 2012. The disclosures were published by WikiLeaks along with French newspaper Liberation and the Mediapart website.
France's foreign minister summoned the US ambassador for a formal explanation in response, while Hollande spoke by phone by with US President Barack Obama, who gave fresh assurances that spying on European leaders had ended.
But Assange accused the US of playing "word games", as it did after revelations of US eavedropping on Merkel.
"What does it matter if they say that they're not going to spy on Hollande personally if they're spying on everyone he talks to?" Assange asked.
"Every single one of these intercepted phone calls that we have published is Hollande talking to someone else, Sarkozy talking to someone else, one of the members of the French government. What does it matter if they say that they're not going to spy on Hollande personally if they're spying on everyone he talks to?"