Polling stations opened at 0600 GMT and the last will close at 1800 GMT with estimated results expected shortly afterward.
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.
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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, only 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.
Hundreds of thousands of French expatriates in the US, Canada and South America cast their ballots on Saturday.
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.
Analysts believe the attack so late in the campaign could shift the focus from the economy to security and hand an advantage to candidates seen as taking a hard line on the issue.
"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 attack, Le Pen called for France to "immediately" take back control of its borders from the EU and deport all foreigners on a terror watchlist.
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