Left-leaning French voters headed back to the polls Sunday to decide whether Francois Hollande or Martine Aubry should take on Nicolas Sarkozy in next year\'s presidential election. Whichever of the pair wins the Socialist Party nomination will immediately become the frontrunner in the race, as polls show the centre-right incumbent trailing either in April and May\'s two-round contest. The vote is also France\'s first US-style open primary -- any elector who says he or she supports the ideals of the left can vote -- and a big turnout could serve as a springboard for the campaign proper. Last Sunday, a bigger than expected 2.66 million voters turned out for the first round, which was won by 57-year-old lawmaker and former party leader Hollande, with only a narrow nine-point lead over Aubry. Voting in the southwestern town Tulle, in his rural constituency, Hollande predicted an even bigger turnout, dubbing this a \"good sign\". \"We have already seen signs in the votes that took place for the French living abroad and in the overseas territories. We have confirmation that there will be a bigger turnout,\" he said. \"The bigger the turnout, the clearer our victory will be and the greater our candidate\'s chance of winning in 2012. It is an important moment, a serious one, even if it\'s not the final moment. That will be May 6, 2012.\" Hollande has won the backing of the four defeated first round candidates, and entered the run-off as favourite, but Aubry mounted a tough fightback this week, branding him a soft centrist without the steel to defeat Sarkozy. Casting her own vote in Lille, where she is mayor, Aubry declared: \"I urge all the French to vote for their convictions and with their hearts for real change.\" Aubry, 61, the former labour minister who gave France is 35-hour working week, has also attacked Hollande\'s lack of executive experience -- he has never served at cabinet level. Hollande has tried to turn the attacks to his advantage, accusing Aubry of undermining party unity and suggesting that his lack of a track record makes it easier for him to run as a candidate of change. Sarkozy\'s camp was wrong-footed by the primary. Some of his supporters grudgingly admit it served as a good shop window for the Socialists, but the president himself dismissed it as alien to French political tradition. Leaders of the ruling UMP have mocked the policies on display in the left\'s primary, portraying them as a throw-back to the 1980s, but all four televised debates between the candidates drew large audiences. The surprise of the first round was the break-through of Arnaud Montebourg, who came in third with 17 percent of votes on a platform of tougher regulation of banks and markets and of protectionism. The right had hoped that the primary format would sow discord between the six hopefuls, triggering the infighting for which the Socialist Party is infamous and hobbling the victor before the general election. In fact, the first round remained relatively civil, despite a history of personal animosity between the frontrunners. Aubry succeeded Hollande as Socialist Party general secretary and has since let it be known that she found the organisation in a sorry state. Hollande was the partner of fourth-placed challenger and defeated 2007 Socialist candidate Segolene Royal for 30 years, raising four children, but split from her before the last race and moved in with his girlfriend. Meanwhile, the whole party was stunned in May when the then favourite for the nomination, IMF chief Dominique Strauss-Kahn, was accused of attempted rape by both a New York hotel maid and a young French writer. Prosecutors have since dropped both investigations, but Strauss-Kahn left the race, pausing only to declare that Aubry agreed not to run if he entered the contest  -- effectively tagging her as a substitute candidate. Despite the bad blood, the campaign only turned truly bitter in the closing straight, when Aubry attempted to close down Hollande\'s narrow but consistent lead by tacking to the left and branding him weak. Historically, both she and Hollande come from the party centre ground. In 1995, when France\'s last Socialist president Francois Mitterrand left office, they were both apostles of modernising former European Commission chairman Jacques Delors -- Aubry is his daughter, Hollande his protege. In all, 9,474 voting stations across France opened at 7:00 am (0500 GMT), and close at 5:00 pm, with partial results expected less than two hours later.