Call for unity
Royal called for unity in the Socialist Party, saying: "I have need of everyone, of everybody's talents, of all the Socialists and this victory is the victory of all the Socialists."
Jacques Chirac, France’s current president, has not ruled out seeking a third term.
However, a serious bid is unlikely given his lack of popular support and his age - he turns 74 on Wednesday.
Nicolas Sarkozy, who leads Chirac's conservative Union for a Popular Movement (UMP), is the only politician on the right who can mount a serious challenge for the presidency.
However, a long-running feud with Chirac has hampered his chances of success.
On the right, Dominique de Villepin, the French prime minister, and Michele Alliot-Marie, the defence minister, are potential rival candidates to Sarkozy, despite possessing less popular support.
Sarkozy has said he will declare his presidential ambitions within the coming days.
Philippe Douste-Blazy, foreign minister, warned against divisions in the ruling party, saying that "... anybody who tries to go against the candidate chosen by the UMP after a debate will be creating a major risk of defeat for our side".
A survey carried out by the BVA institute, published on Thursday, found that 42 per cent of French voters thought Royal would make a better president than Sarkozy, who had 36 per cent support.