Former French Labor Minister Martine Aubry has conceded defeat to Francois Hollande in the Socialist Party primary election to pick a challenger to President Nicolas Sarkozy.
Aubry gave up Sunday when partial results gave her 44 percent of the vote compared to 56 percent for Hollande, who won last week's first round.
She congratulated her challenger and said she will put all her energy into making sure Hollande defeats Mr. Sarkozy in next year's general election.
Sunday's Socialist Party vote was the first U.S.-style primary election in French history. Hollande is a veteran moderate Socialist. Many in France believe he may be the best candidate to defeat the increasingly unpopular Mr. Sarkozy and tackle France's tough economic challenges.
Mr. Sarkozy is widely expected to seek a second five-year term. Political analysts consider him vulnerable, noting that many French voters are unhappy with his economic policies.
Not appearing on Sunday's Socialist ballot was former International Monetary Fund chief Dominque Strauss-Kahn. He had been favored to win the party's nomination until his candidacy was derailed in May by rape charges by a New York City hotel maid. The charges were dropped, but experts believe Strauss-Kahn's political career may be over.