The first-round balloting will trim down a list of 10 candidates from across the political spectrum to two finalists for a May 6 runoff. Polls have shown that many voters are turned off by Sarkozy's flashy style as they worry about jobs and the economy.
The Interior Ministry said early turnout figures showed 28 per cent of France's 44-million-plus voters cast ballots before noon, less than the 31 percent in 2007 at the same time, but more than in the four previous races.
Sarkozy and his main expected challenger, Socialist nominee Francois Hollande, have pushed for a strong turnout on the idea that it would help the political mainstream and dilute the impact of more ideological voters.
Polls for months have shown that Sarkozy and Hollande are likely to make the cut, and suggest Hollande would win the campaign finale.
"This is an election that will weigh on the future of Europe. That's why many people are watching us," said Hollande after voting in Tulle, a town in central France. "They're wondering not so much what the winner's name will be, but especially what policies will follow."
"That's why I'm not in a competition just of personalities. I am in a competition in which I must give new breath of life to my country and a new commitment to Europe," he added, urging a big turnout from voters.
Sarkozy waved to supporters and apologized to polling station attendants "for the big fuss" as he voted at a high school in posh western Paris along with his wife, Carla Bruni-Sarkozy _ and a throng of journalists in tow. Behind barriers, a small crowd chanted "Bravo! Bravo!" as they left. He didn't speak to the media on the way out.
Sarkozy, defending his record on the campaign trail, has repeatedly pointed to a tough economic climate and debt troubles across Europe _ not just in France.
But with turnout a looming question, surprises could await among candidates including far-right nationalist Marine Le Pen, Communist-backed firebrand Jean-Luc Melenchon or centrist Francois Bayrou.
While they are not expected to win, a strong performance by one or all of them could cast a shadow over the second round vote. Polls show the five other candidates are expected to receive low single-digit percentages.
Balloting got under way Saturday in France's embassies and overseas holdings. Polls have shown that concerns about jobs _ with the unemployment rate hovering near a 10-year high _ and the economy are top issues.
France was one of six countries that in the 1950s that founded the predecessor of the European Union. It's the eurozone's second-largest economy after Germany.
Sarkozy and German Chancellor Angela Merkel, a tandem that some call "Merkozy", have championed a treaty on budget austerity for the 17-nation eurozone. But Hollande wants the treaty to also address state support for economic growth, not just cost-cutting, arguing that's the only way for Europe to recover.
At a time when voters across Europe have ousted incumbents amid the economic woes, a Hollande victory would tilt the continent's political balance to the left as EU states such as Greece, Italy, Ireland and Spain work to wriggle their way out of crushing state debts.
As for international policy, candidates of many stripes want to bring France's 3,600 troops home from the NATO-led mission in Afghanistan, and Hollande has vowed a fast timetable: A pullout by the end of this year.
The campaign has often centered on hot-button issues such as immigration, Islam in France, and calls for taxes on the rich _ which experts suggest will, in fact, have little effect on France's high state budget deficit.
TV images showed Hollande and several other candidates voting at polling stations around France. Some voters expressed disappointment about the crop of presidential aspirants, while others say France needs a new track.
"I think most people are not satisfied with the last five years, people want change, especially in terms of job creation," said voter Eli Lazovsky, a 38-year-old hotel manager, after casting a ballot in a well-to-do Paris neighborhood off the Champs-Elysees.
Hollande, in his Mr. Nice Guy kind of way, has tapped into a fear of the free market that has always held more sway in France than almost anywhere in the West, and has enjoyed a resurgence in the era of Occupy Wall Street and anti-banker backlash.
Hollande wants to tax high-income earners at 75 percent and reconsider a hard-won European fiscal treaty meant to stem the continent's debt crisis. He says it's too focused on cost-cutting and hurts ordinary folks.
More than anything else, this campaign is a referendum on the man currently in charge: Sarkozy inspired voters in 2007 with pledges to break with the past and make France a more dynamic economy.
After an initial wave of reforms, his momentum fizzled. His stormy personal life got in the way: He divorced months into office, then quickly married former supermodel Bruni and became seen as a bling-bling president more concerned with pleasing his super-rich friends than serving the public.
But municipal employee Marie-Francaise Gouyet, 55, said she didn't believe the polls that suggested that Sarkozy is likely to lose to Hollande in the second round. She said she favored the president's economic policies.
"We don't have the choice, we have to stick to austerity," she said, adding that she voted for Sarkozy. "'Sarko' put in place important reforms like for pensions. He has a good record for his first 5 years."
Entrepreneur Mohammed Derisse, 37, who backs Hollande, countered: "We can't spend much more money. But the president has to do it with less pressure. Sarkozy was too much pressure. Hollande wants to do it in a soft way, not hurt the people."
The presidential election will determine the make-up of the next government and will finish just a month before elections for the National Assembly that is currently controlled by Sarkozy's conservatives.
Turnout in the 2007 first round was nearly 84 percent, the highest figure since the 1970s. Sarkozy is battling to avoid becoming France's first one-term president since Valery Giscard d'Estaing lost to Socialist Francois Mitterrand in 1981.
Sarkozy has said he'll pull out of politics if he loses.