PARIS (AP) -- France voted in a presidential run-off election on Sunday that could see Socialist challenger Francois Hollande defeat incumbent Nicolas Sarkozy by capitalizing on public anger over the government's austerity policies.
The election outcome will impact efforts to fight France's debt crisis, how long the nation's troops stay in Afghanistan and how France exercises its military and diplomatic muscle around the world.
Hollande voted in his electoral fief of Tulle, in central France. Live television coverage showed the 57-year-old politician shaking hands and chatting with voters on his way into the polling station.
"It's going to be a long day," Hollande told reporters gathered to watch him vote. "It's up to the French people to decide if it's going to be a good day," he said.
Sarkozy, accompanied by first lady and former supermodel Carla Bruni-Sarkozy, voted at midday in Paris' 16th arrondissement. Scores of television cameras surrounded the couple, and members of the public could be heard chanting "Sarkozy! President!" But Sarkozy, 57, chose not to speak on live TV.
Under Sarkozy, France pledged to rein in its spending while the rest of 17 countries that use the euro embark on a strict period of belt-tightening. In France, that has included programs designed to reduce government employment.
Sarkozy, disliked by many voters for his handling of the economy and brash personality, promised he could produce a surprise victory on Sunday. Speaking on Europe-1 radio Friday, he said much will depend on whether French voters bother to cast ballots in an election that polls have always predicted Hollande would win.
Turnout was a suprisingly high 79 percent in the first round April 22, and polls suggested that Sarkozy's best chance of an upset would come from even greater voter turnout Sunday.
Preliminary figures from the Interior Ministry suggested voters were turning out in greater numbers. At 1000 GMT (6 a.m. EDT), turnout was 30.66 percent, up from 28.29 percent at the same time two weeks ago.
Polling stations opened in mainland France at 0600 GMT (2 a.m. EDT) Sunday, a day after voting got under way in France's overseas territories. Preliminary results in the French election are expected around 1800 GMT (2 a.m. EDT) Sunday.
French law bars the publication of results before all polling stations have closed to avoid swaying the outcome, and the fine for doing that is euro75,000 ($98,145). Still, many expect Sunday's election results to be leaked early via Twitter or other online methods, as they were during the first round two weeks ago.
Asked Friday what he would do if he loses, Sarkozy said simply: "There will be a handover of power."
"The nation follows its course. The nation is stronger than the destiny of the men who serve it," he said. "The fact that the campaign is ending is more of a relief than a worry."
Hollande was benefiting from anti-Sarkozy fervor, with some voters saying their choice was more a vote against him than one for Hollande.
Stephanie Debaye, 32, said she was voting for "the departure of Nicolas Sarkozy."
"On behalf of my compatriots, I felt quite insulted. He was so aggressive. I hope things will calm down," Debaye said outside a polling station in Paris.
Another Paris voter highlighted this anti-Sarkozy vote, saying she's backing Hollande, even though his program is "suicidal."
"He'll raise the minimum wage, increase civil servants. But France is already in debt," said Florence Macrez. His fiscal reform project will only increase the pressure especially on the middle class, she added.
Nearby the Socialist Party headquarters in central Paris, Sunday morning churchgoers said the next president must focus first on fixing France's sputtering economy.
"We hope that the next president will fix the economical position of France which was not properly handled by the previous president," said Dominique Grange, a retiree.
In a sign of the attention the campaign has attracted, Google's home page in France was redesigned with one of its ever-changing "doodles" devoted to the election.
In Hollande's town of Tulle, residents who got up early to vote offered mixed messages about him. He has been a local official and lawmaker for years in the town and its surrounding Correze region.
"I don't know if he's capable of being president. I just don't know because here we just bump into him on the street. With us, he's like that," said Lydia Sobieniak, 65, a former factory worker, outside the polling station where Hollande was voting shortly after it opened.
"It's going to be hard. Whoever it is (who wins) ... there will be no miracles," said Sobieniak, who added that Hollande helped her get a contract job in education in 2004 after she left her private sector job.
Hollande beat Sarkozy by about half a million votes in the first round of voting on April 22, which saw 10 candidates competing for the job of running this nuclear-armed country with a permanent seat on the U.N. Security Council for the next five years.
Hollande urged his followers against complacency. "Victory is within our grasp!" he said in a rousing rally in the southern city of Toulouse on Thursday night.
Polls released Friday and Thursday showed the gap between the candidates shrinking but results still solidly in Hollande's favor. The polls were carried out after the candidates' only debate Wednesday night, which Sarkozy had hoped would be the knockout blow he needed.
Hollande has received the support of a prominent centrist who won 9 percent of the vote in the first round of presidential elections, Francois Bayrou. Bayrou said Thursday night he would not give his voters specific guidance for Sunday's vote - but that he will cast a ballot for Hollande.
Bayrou criticized Sarkozy's campaign rhetoric as too violent. Sarkozy has sought to lure far-right voters who supported anti-immigrant candidate Marine Le Pen in the first round.
Sarkozy kept it up anyway Thursday at a big campaign rally in Toulon.
"We don't want different tribes, we don't want ethnic communities to turn in on themselves, we don't want (non-citizen) immigrants to vote," he said.
Critics of Sarkozy have often faulted him for his brash style, alleged chumminess with the rich, and inability to reverse France's tough economic fortunes and nearly double-digit jobless rate.
Hollande has promised more government spending and higher taxes - including a 75-percent income tax on the rich - and wants to re-negotiate a European treaty on trimming budgets to avoid more debt crises of the kind facing Greece.
Jamey Keaten in Tulle, France, and Paolo Santalucia, Sarah DiLorenzo and Elaine Ganley in Paris contributed to this report.