Ms Aubry appeals to traditionalists within the Socialist Party
French ex-presidential candidate Segolene Royal is contesting the results of a vote to choose the leader of the French Socialist opposition.
Martine Aubry, a former minister and current mayor of Lille, won the vote by a razor-thin margin of 42 votes.
Ms Aubry is best known as the architect of the 35-hour work week.
Supporters of Ms Royal said there had been irregularities and demanded a re-run of the vote next week, raising the prospect of more party in-fighting.
The party has been divided over whether to move toward the political centre or hold to traditional leftist beliefs.
Ms Aubry, 58, won 50.02% in a second ballot of party members. Ms Royal scored 49.98%.
Ms Royal's lawyer, Jean Pierre Mignard, said the result was "contested and questionable".
"I am not going to take this," Ms Royal told AFP news agency.
But Ms Aubry rejected her proposal to hold a new vote. She will be the first female to head the French Socialists.
She takes over from Francois Hollande, Ms Royal's estranged partner and the father of her four children, who has led the Socialist Party for the past 11 years.
The election went to a second round after a first ballot on Thursday failed to produce a winner with more than 50% of votes.
Ms Royal gained 42.5% of the vote, Ms Aubry 34.7% and Leftist MEP Benoit Hamon 22.8%.
Mr Hamon dropped out and urged those who had backed him to vote for Ms Aubry in the second round.
Ms Aubry has said she wants to reform the party while also upholding its "leftist values".
Ms Royal, defeated by centre-right President Nicolas Sarkozy in last year's election, had said she wanted to renew the party and put it in a position to beat the conservative candidate in 2012.
There has not been a Socialist president since Francois Mitterrand won a second term in 1988.
Ms Royal has been accused of seeking to transform the party into her own personal electoral machine, says the BBC's Emma Jane Kirby in Paris.
Supporters had hoped she could reform the party and bring it towards the centre, but critics, especially among the party's old guard, have accused her of being politically inconsistent.
The voting took place after last weekend's annual party congress - that was meant to back a single candidate - ended in disarray, with top party members failing to reach consensus on a new leader.
France's media have said the Socialists showed themselves at the Reims convention to be "ungovernable".