Far-right leader Marine Le Pen and centrist Emmanuel Macron are the favourites to progress to a run-off on May 7 but the result is too close to call in a deeply divided country.
Le Pen, the 48-year-old leader of the National Front (FN), hopes to capitalise on security fears that were catapulted to the fore of the campaign after the fatal shooting of a policeman on Paris's Champs Elysees avenue claimed by the Islamic State group.
Aiming to ride a wave of populism that led Donald Trump to the White House and Britain to vote for Brexit, Le Pen also wants to pull France out of the eurozone and has threatened to take the country out of the EU as well.
Her ambitions have led observers to predict that a Le Pen victory could be a fatal blow for the EU, already weakened by Britain's vote to leave the bloc.
Macron, 39, is seeking to become France's youngest ever president and has campaigned on a strongly pro-EU and pro-business platform.
Seeking to benefit from a worldwide move away from established political parties, the former banker and economy minister formed his own movement, "En Marche" ("On the Move"), that he says is "neither to the left nor to the right."
But polls show scandal-tainted conservative candidate Francois Fillon, a former prime minister, and hard-left firebrand Jean-Luc Melenchon are also in with a fighting chance of finishing among the top two candidates and reaching the all-important second round.
Polling stations opened at 0600 GMT and the last will close at 1800 GMT with estimated results expected shortly afterwards.
Attack effect
In the wake of the policeman's killing on Thursday, 50,000 police and 7,000 soldiers have been deployed around France to protect voters.
The terror attack was the latest in a bloody series have cost more than 230 lives since 2015.
Anne Piechaud, a 59-year-old architect who was taking a train from Paris early Sunday to vote in the western city of Bordeaux, brushed aside the security fears.
"It has had no effect on my vote. The candidates have not talked about it in their manifestos and anyway, you're not completely safe anywhere in the world these days," she told AFP.
Analysts believe the attack so late in the campaign could hand an advantage to candidates seen as taking a hard line on security issues.
"If it were to benefit someone, that would clearly be Marine Le Pen who has dominated this issue throughout the campaign, or Francois Fillon," said Adelaide Zulfikarpasic of the BVA polling institute.
In the aftermath of the shooting, Le Pen called for France to "immediately" take back control of its borders from the EU and deport all foreigners on a terror watchlist.
US President Donald Trump tweeted that the shooting "will have a big effect" on the election.
Closely watched around the world, the French campaign has been a rollercoaster ride of unpredictable twists and turns.
A race that began with the surprise nomination of Fillon as right-wing candidate in November shifted into a higher gear in December when unpopular Socialist President Francois Hollande decided not to seek re-election.
Hollande's five years in office have been dogged by a sluggish economy and the constant terror threat.
Fillon was the early frontrunner until his support waned after he was charged following accusations he gave his British-born wife a fictional job as his parliamentary assistant for which she was paid nearly 700,000 euros ($750,000) of public money.
Though there are four main contendersin the election, a total of 11 candidates are taking part, most polling in single digits.
The candidate for the governing Socialists, Benoit Hamon, was a distant fifth going into the final weekend.
In such a close-fought race, the quarter of French voters still undecided on the eve of voting could play a crucial role in the outcome.
"I don't like any of them, they're all disappointing," 73-year-old Ghislaine Pincont said in the northern city of Lille on Saturday.
"At worst, I'll cast a blank vote."
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