The apparent rejection calls into question the pope's reputation as holding more liberal views on homosexuality.
Laurent Stefanini, 54, a senior diplomat and Mr Hollande's chief of protocol, was nominated in early January but the Vatican has maintained a stony silence over whether it accepts his credentials, officials in Paris said.
The usual time frame for their acceptance is a month and a half. After that, a prolonged silence after a nomination is normally interpreted as a rejection.
The Elysee said that the choice of Mr Stefanini to represent France at the Vatican resulted from "a wish by the president and a cabinet decision" and that the president regarded him as "one of our best diplomats."
French media widely reported that Mr Stefanini has been blackballed due to his homosexuality.
Le Journal du Dimanche quoted a Vatican insider as saying that the rejection was "a decision taken by the pope himself."
Liberation, the left-leaning daily, said that "the Vatican's homophobia seriously tarnishes Pope Francis' image as being (slightly) more open-minded that his predecessors on sexuality".
France in 2007 nominated a gay ambassador to the Vatican who had a partner recognised under French law but the Holy See never responded to the nomination, despite lengthy attempts to secure him the post.
France's President Francois Hollande (L) shakes hands with Laurent Stefanini (Bertrand Langlois/AFP/Getty Images)
Mr Stefanini is reportedly widely respected by many in the Catholic Church, following his previous stint as number two in the French embassy at the Vatican from 2001 to 2005. Very discreet about his private life, he is "highly thought of in Roman circles," said Antoine-Marie Izoard, a Vatican specialist with the I-Media press agency.
Cardinal Andre Vingt-Trois of Paris reportedly interceded personally with the Pope to back his nomination. La Croix newspaper said Cardinal Jean-Louis Tauran, the former Vatican foreign minister who is currently president of the Pontifical Council for Interreligious Dialogue, also supports the appointment.
Pope Francis has to date adopted a considerably softer line on homosexuality than his predecessor Benedict XVI.
"If a person is gay and seeks God and has good will, who am I to judge?" the pontiff said two years ago, adding that gay people should not be marginalised but integrated into society.
However, that did not stop him criticising the current French Socialist government passing a law in 2013 legalising gay marriage and adoption rights for gay couples, leading to mass protests from among the country's Catholics.
He also compared transsexuals to "nuclear weapons" in a book this year, saying both "do not recognise the order of creation".
Some at the Vatican reportedly saw this latest nomination as a "provocation".
Observers say the Pope cannot be seen to be adopting an overly gay-friendly approach that would shock the Catholic church's more conservative elements