The left has not won a presidential election in a quarter of a century, but with France mired in low growth and rising joblessness, opinion polls show Socialist challenger Francois Hollande beating the right-wing incumbent.
Sunday's vote will whittle the field from 10 to two, and Hollande and Sarkozy are expected to face each other head-to-head in a May 6 run-off to decide who runs France, a nuclear power and Europe's second largest economy.
Hollande says Sarkozy has trapped France in a downward spiral of austerity and job losses, while Sarkozy says his rival is inexperienced and weak-willed and would spark financial panic through reckless spending pledges.
The eurozone debt crisis and France's sluggish growth and high unemployment have hung over the campaign, with Sarkozy struggling to defend his record and Hollande unable to credibly promise spending increases.
Hollande voted in his stronghold, the country town of Tulle in the central Correze region, where he is the local member of parliament and heads the regional council and was warmly greeted by officials and voters alike.
"I am attentive, engaged, but first of all respectful," he told reporters. "The day ahead will be a long one, this is an important moment."
Sarkozy and his former supermodel wife Carla Bruni voted in Paris' plush 16th district, a stronghold of his right-wing UMP party.
Polling began Saturday in France's far-flung overseas territories, and got underway on the European mainland at 8.00am (0600 GMT) on Sunday. It was to continue until 6.00pm in most of the country, and 8.00pm in major cities.
French polling agencies are permitted to take samples directly from ballot boxes, so accurate voting estimates are made public immediately polls close.
More than 44 million voters are registered but pollsters predict around around 25 percent will abstain, a high level by the standards of a French presidential poll and a source of worry to the candidates, especially Hollande.
Early turnout figures for the Atlantic island of St Pierre showed voting down six percent compared to the 2007 race. Voting was also down by about one percent in Martinique, but it was up two percent in French Guyana.
France is proud of its republican democratic tradition, and the press marked polling day with appeals for a high turnout. "To the voting booths!" declared the newspapers Ouest de France and Voix du Nord.
"At last, we can vote!" declared L'Alsace.
In all, ten candidates are in the race, Hollande and Sarkozy being trailed by far-right flag-bearer Marine Le Pen, hard-left firebrand Jean-Luc Melenchon, veteran centrist Francois Bayrou and a handful of outsiders.
The campaign has run on for months but has yet to inspire much passion, except for a series of mass open-air rallies by supporters of Melenchon, whose Communist-backed Left Front coalition has made a strong breakthrough.
An average of the last eight polls released ahead of the end of first round campaign at midnight on Friday showed Hollande winning the first round with an average of 28 percent support, against 26.4 percent for Sarkozy.
Far-right candidate Marine Le Pen was third with an average of 15.75 percent, followed by Communist-backed Jean-Luc Melenchon of the Left Front with 13.75 percent and centrist Francois Bayrou with 10.1 percent.
Opinion polls and campaigning were banned from midnight on Friday, and will restart on Monday in the build-up to the May 6 run-off, which Hollande is expected to win by around 55 percent to 45.
Once the first round is out of the way, Sarkozy and Hollande will face each other in a two week scramble for the line, including a head-to-head televised debate that could be the incumbent's last chance to change his fortunes.
Privately, Sarkozy's top supporters have begun to admit that if Sarkozy fails to regain the momentum and slip ahead of Hollande on Sunday, he will have too much ground left to make up before the May 6 showdown.
AFP