However, Ms Royal’s supporters have claimed there were irregularities in the process and have called for a re-run of the vote next week, which is likely to spark more in-fighting within the party’s ranks.
The French Socialists have had problems with division amongst its members, who fail to agree on the future aims of the party.
58-year-old Ms Aubry won by 50.02% in a second ballot of Socialist Party members, whilst her rival Ms Royal lost with 49.98% of the votes.
Ms Royal's lawyer, Jean Pierre Mignard, has questioned the result and Ms Royal was reported by AFP news agency as saying: "I am not going to take this."
Ms Aubry has, however, turned down the suggestion that there should be a new vote.
