Mr Assange denies the assault claims and has been living at the Ecuadorean embassy in London since 2012.
Earlier on Friday, France`s Le Monde newspaper published an open letter Mr Assange had written to President Francois Hollande asking for asylum.
In it, he wrote: "By welcoming me, France would carry out a humanitarian and symbolic gesture, sending encouragement to every journalist and whistleblower."
He also said his life was in danger.
A statement from Mr Hollande`s office said it had reviewed the request and decided not to grant Mr Assange asylum.
"The situation of Mr Assange does not present any immediate danger," the statement said. "Furthermore, he is subject to a European arrest warrant."
Mr Assange - an Australian journalist and activist - has not been formally charged, but prosecutors want to question him over allegations of rape and sexual misconduct made by two women he met during a trip to Sweden in August 2010.
He claims the allegations are part of a plot to extradite him to the US because of Wikileaks` publication of thousands of classified US documents earlier in 2010.
But the former computer hacker has not been charged with any crime in the US and the Americans have not issued the UK with an extradition request.
Ecuador offered Mr Assange asylum in August 2012, shortly after he sought refuge at the country`s embassy in London
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