Christine Lagarde has been a member of the French synchronized swim team, an intern to then-Rep. William S. Cohen (R-Maine) and the head of the Chicago-based international law firm Baker & McKenzie. Since 2007, as France’s stylish and plain-spoken finance minister, she has charmed TV host Jon Stewart, French voters and international financiers alike.

Now Lagarde will need all of her skills in a campaign to become the managing director of the International Monetary Fund, the Washington-based institution that aids countries staggering under huge fiscal deficits, towering national debts and shaky banks.

“If I’m elected, I will bring all my expertise as a lawyer, a minister, a manager and a woman” to the IMF, she said Wednesday as she announced her candidacy in Paris.

Lagarde, 55, would be the first woman — and first non-economist — to run the male-dominated fund. Her appointment could help alter the institution’s culture after Dominque Strauss-Kahn, the previous managing director and presumptive Socialist Party presidential candidate, was forced to resign this month after being charged with sexual assault.

In recent days, European leaders have coalesced behind Lagarde’s candidacy. Her supporters call her a formidable negotiator, a key to uniting a bickering Europe in the quest to save the euro and manage the debt crisis that has rocked the continent over the past 18 months.

“She’s not from the priesthood of world-class economists,” said Mark Medish, a senior Treasury official under President Bill Clinton who has known Lagarde for a decade.

“Like a good lawyer, she’s learned her finance ministry brief, but she brings a broader perspective than many of her peers in other countries,” he said, “something that goes beyond the arithmetic of tax and revenue policy. That accounts for her success and popularity.”

But in other ways, Lagarde would be an all-too-familiar choice for the IMF’s top job. France has supplied four of the 10 managing directors in the history of the fund, which was created in 1944. French officials have run the IMF for 25 of the past 38 years. (An American traditionally gets the top post at the World Bank.)

On Tuesday night, IMF executive directors representing Brazil, China, India, Russia and South Africa called for “a truly transparent, merit-based and competitive [selection] process” that they said “requires abandoning the obsolete unwritten convention that requires that the head of the IMF be necessarily from Europe.”

“I think that this is a moment not to have a European as head of the IMF,” said Luigi Zingales, a finance professor at the University of Chicago. “The time has come to make these institutions more international and not just leftovers from World War II.”

A list of respected alternatives is being bandied about, including Mexican central banker Agustin Carstens, a former senior IMF official with a PhD from the University of Chicago, who declared his candidacy this week. Other ministers or central bankers from Brazil, India, Malaysia and South Africa are considered qualified contenders.

Yet Lagarde has attained front-runner status. Returning to the U.S.-based IMF would be a homecoming of sorts for her. She became well known in Washington and New York while heading Baker & McKenzie. Earlier she attended the Holton Arms School in Bethesda. She speaks fluent English.

In her native France, Lagarde is a popular figure whose off-the-cuff manner has sometimes landed her in trouble. Asked during a radio program in 2008 what people could do about high gas prices, she said: “Ride a bike.”

In 2009, she won rousing applause on Stewart’s “The Daily Show” for her tough talk against bankers — then won laughs for taking out a French beret for Stewart. “Viva la France! Viva la Christine Lagarde!” Stewart exclaimed.

Dominique Moisi, a founder of the French Institute for International Relations in Paris and a longtime acquaintance of Lagarde’s, said, “She’s mastered one of the things which is not common in France, to be a respected and popular politician, but also have a sense of humor,” he said. “She gives the impression of gravitas and seriousness without being arrogant.”

In the new HBO movie “Too Big to Fail,” an actress portraying Lagarde scolds then-Treasury Secretary Henry M. Paulson on the phone in 2008 for letting Lehman Brothers go bankrupt. In real life, Lagarde is more tactful, at least in public. The first lesson of Lehman’s collapse, she said in Washington in October 2008, was “humility,” adding that she didn’t want to blame anyone, “certainly not Hank.” But then she said restoring markets should take precedence over punishing specific firms. “The moral hazards have to be dealt with at a later stage,” she said.

“The markets need different rules and better rules,” she said. “A lot of the difficulties are the result of an absence of rules.”

Last year, she backed a far-reaching rescue plan to both bolster a tottering Greece and protect the rest of the euro zone. “We are all Greek,” she said in an interview then. After tense negotiations, she said a deal was made that “was Italian pasta, German sausage and French wine.”

Many economists say she is too soft on banks. Zingales criticizes Lagarde as reluctant “about taking a pound of flesh from creditors” of struggling governments. Simon Johnson, a former IMF chief economist, complains that she opposed higher capital requirements for banks. He laments that she has not embraced a restructuring of loans for Greece, calling her approach “extend and pretend” to avoid forcing large write-offs at French banks.

“We’re ruling it out in any form,” she said when the French newspaper Le Figaro asked her about Greek restructuring this month. She pressed the Greek government to privatize state-owned assets instead.

Although some Europeans say they need one of their own to persuade reluctant policymakers, Johnson said: “You need someone with more distance.”

In the IMF’s voting system, which gives more weight to the largest economies, Europe has about a third of the votes needed. The United States has 17 percent.

President Obama, in Europe on a number of state visits, is expected to be lobbied by British, French and German officials to back Lagarde.

Lagarde’s candidacy remains clouded by a judicial inquiry into whether she improperly moved a court case involving the sale of the sportswear company Adidas to an arbitration proceeding. In the end, French tycoon Bernard Tapie, a close ally of President Nicolas Sarkozy, received $400 million. A report on Lagarde’s intervention is expected soon.

With new fears of default by near-bankrupt Greece and anxiety about more major European economies, Europeans are arguing that Lagarde would represent a seamless transition from Strauss-Kahn, who pushed the IMF to lend emergency money more rapidly in times of crisis.

She has minced no words about one flaw she sees in big banks: too many men.

“Gender-dominated environments are not good . . . particularly in the financial sector, where there are too few women,” she told Britain’s Independent newspaper in February. “Men have a tendency to . . . show how hairy-chested they are, compared with the man who’s sitting next to them. I honestly think that there should never be too much testosterone in one room.”

Mufson reported from Washington.