Royal, who currently leads opinion polls for the left, threw her hat into the ring for the elections in April at a socialist meeting in Vitrolles, southern France, on Friday.
She said: "I accept taking on this mission for the benefit of France and the trials that go with it, even as I want to protect my family, and so I present myself for the vote of the Socialists, and then I hope for the judgement of the French people in winning, on merit, their confidence in April 2007.
"Accomplishing the profound changes which are hoped for, representing the nation and ensuring that the state functions well, that is the task which awaits us."
She pledged to "revive the country" and "give it every opportunity" against a right-wing she accused of wanting to "unmake France".
Royal, head of the Poitou-Charentes regional council and a former minister, was boosted this week by an opinion poll saying 54 per cent of Socialist Party (PS) supporters backed her.
The PS, led by Royal's partner Francois Hollande, the father of her four children, is to designate its presidential candidate after a vote of some 200,000 party members on November 16, with a possible second round a week later.
Royal's main socialist rivals are Dominique Strauss-Kahn, the former finance minister who entered the race earlier on Friday, and former prime minister Laurent Fabius, who declared himself a candidate as far back as January.
Former culture minister Jack Lang is also a contender, while ex-prime minister and unsuccessful presidential candidate in both 1995 and 2002, Lionel Jospin, withdrew on Thursday.
Amongst those on the right of French politics, Nicholas Sarkozy, who leads the governing UMP party, is expected to be a contender in next year's presidential election.