Assange, in a letter to the French President described himself as a "journalist pursued and threatened with death by the United States' authorities as a result of my professional activities".
He asked in the letter, published on Friday in Le Monde newspaper, to be granted asylum by France.
Just few hours later, the office of President Francois Hollande responded in a statement that read: "France cannot act on his request".
"The situation of Mr Assange does not present an immediate danger. Furthermore, he is subject to a European arrest warrant," Hollande's office said.
Assange, who turned 44 on Friday, has spent over three years holed up in Ecuador's embassy in London to avoid extradition to Sweden, where he faces allegations by two women, one of rape and one of sexual assault, which he denies.
The former computer hacker fears extradition to Sweden could lead to him being transferred to the US to face trial over WikiLeaks' publication of classified US military and diplomatic documents.
