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.
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.
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."
Le Pen cast her ballot in Henin-Beaumont, a former coal mining town in northern France that has an FN mayor.
Macron voted in the chic Normandy seaside resort of Le Touquet with wife Brigitte, his former high school teacher who is 25 years his senior.
Nearly 47 million people are eligible to vote and most polling stations will close at 1700 GMT with those in major cities shutting an hour later. First projected results are expected shortly afterwards.
The terror attack was the latest in a bloody series have cost more than 230 lives since 2015.
Guy Belkechout, a 79-year-old pensioner who was voting in the working-class Parisian suburb of Trappes, said he was concerned.
"Security issues have influenced me after the attacks. Candidates who want fewer security measures, who want to reduce the police's powers, have not got my vote," he told AFP.
But Yanis Olive, a 35-year-old photographer voting in Paris, said security was not "a major issue" -- unemployment and the economy were more important.
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.
Closely watched around the world, the French campaign has been full 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 (USD 750,000) of public money.
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.
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