“Gazelles,” she said last May, “run faster than elephants.”

Responding to voters’ disillusionment with traditional elitist politics, she is promising more power to the people, giving local governments more authority, subsidizing small businesses, creating affordable housing and encouraging citizens to submit their ideas online, for example.

Even her opponents agree that her looks help. Published photos of her in a bikini while on vacation underscored her youthfulness and glamour, while in poll after poll, her telegenic smile and elegant profile have appealed to a French public yearning for a new style of leadership.

Ms. Royal, president of the Poitou-Charentes region in the west, has also cultivated an image as a grass-roots nurturer, taking her campaign to the countryside to listen to concerns about social issues such as educational reform and youth crime.

With a portfolio that includes stops at three second-tier ministries — Environment, School Education and Family and Childhood — Ms. Royal has been criticized as lacking the experience and gravitas to lead a country that is a nuclear power.

Her inexperience in foreign policy issues surfaced last week when she said during the last campaign debate that Iran should never be allowed to have a civilian nuclear energy program. As her opponents quickly pointed out, Iran enjoys that right as a signatory to the Nuclear Nonproliferation Treaty.

But the party members’ enthusiasm for Ms. Royal seemed to trump any slips on policy issues.

“Her victory means that the Socialist Party is still under the shock of April 2002 and is looking above all for a candidate who can win,” said Dominique Reynié, a professor of political science at the Institut d’Études Politiques in Paris. “Much more important than a doctrine or a program is the look of a champion.”

In the April 2002 presidential election, the Socialist candidate, Prime Minister Lionel Jospin, was eliminated in the first round, trailing even the far-right National Front candidate, Jean-Marie Le Pen.