If elected, Hollande would be France's first left-wing president since Francois Mitterrand left office in 1995.
Ms Royal graduated in 1980 and, along with Mr Hollande, became an adviser to Socialist President Francois Mitterrand.
He is now aiming to become France's first left-wing leader since the late Francois Mitterrand left office in 1995.
Royal's defeat is a severe blow for French socialists, who have not held the presidency since Francois Mitterrand's last term ended in 1995.
There have been moving history moments, like in 1984, when Francois Mitterrand and Helmut Kohl held hands at a World War I cemetery in Verdun.
And is there hope that President Obama will see the light and tack to the center on economic policy, as did Francois Mitterrand and Bill Clinton?
During the term of office of the late socialist President, Francois Mitterrand, illicit commissions were paid on other business deals for French companies in Africa, Latin America and Europe.
" We are in the room with the monkey (Francois Mitterrand's former office) sitting on Owens's Alchemist chairs a triangular affair that he describes as "meant more for perching than for reading.
WSJ: Designer Rick Owens's Paris Home | WSJ. Magazine May 2013
Mr Hollande - the first Socialist to win the French presidency since Francois Mitterrand in the 1980s - earlier gave his victory speech in his stronghold of Tulle in central France.
BBC: Francois Hollande to set France on new course after win
Jacques Attali, a French economist and former adviser to the late president Francois Mitterrand, warned of a Europe in danger of "falling asleep", of young people being excluded from a changing world.
JARNAC, France (CNN) -- In ceremonies befitting both his position of power and his humble roots, former French President Francois Mitterrand was honored Thursday by world leaders in Paris and by his birthplace of Jarnac.
German Chancellor Helmut Kohl, UK Prime Minister John Major and French President Francois Mitterrand toasted their agreement to pursue European Monetary Union over a lunch of lobster in a lemon and courgette chutney, followed by pheasant.
London-based Anton Mosimann, a visiting chef to 10 Downing Street who has cooked for a string of British prime ministers, recounts how Margaret Thatcher once asked for a lavish meal to entertain the then French President Francois Mitterrand.
Several French presidents have been accused of glossing over health problems, notably Georges Pompidou, who died of cancer while in office in 1974, and Francois Mitterrand, who concealed that he was diagnosed with cancer in 1981, only months after first being elected.
Given the constraints of international finance and economic structures, observers say that if Hollande is elected president he will not really have the room to maneuver to radically shift France to the left the way his Socialist predecessor Francois Mitterrand did three decades ago.
As the commemorative roses pile up outside the door of the apartment where Mitterrand died, and the true believers express their emotions for the cameras, it seems clear that, for at least the first year, Francois Mitterrand has successfully managed his image beyond the grave.
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