Independent centrist Emmanuel Macron will face far-right Marine Le Pen in a run-off on 7 May
Mr Macron, a 39-year-old who has never fought an election before, tells jubilant supporters: "In one year, we have changed the face of French politics"
Marine Le Pen called on "all patriots" to join her and "concentrate on what is essential - the survival of France"
The beaten candidates from mainstream parties, Socialist Benoît Hamon and conservative François Fillon, declare support for Mr Macron
In an election day editorial in Le Figaro, external, senior editor Paul-Henri du Limbert reminds voters of Thursday's attack in Paris, saying that France is "at war" with Islamic militancy.
"Faced with such a threat, the next president will have to be implacable," he writes.
Image source, Le FigaroBBC correspondents are out and about in France as voting gets underway.
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Image source, AFP/GettyExtra security measures are in place for the election after Karim Cheurfi, a convicted criminal, shot a police officer in the head on the Champs Elysees in Paris on Thursday.
Cheurfi was killed by security forces and a note defending the so-called Islamic State group was found near his body.
National security had been one of the main talking points during the campaign, but candidates have been accused of exploiting the most recent attack for political gains.
About 50,000 police and 7,000 soldiers are being deployed across the country to secure polling.
One of the earliest voters was Penelope Fillon, the wife of conservative candidate François Fillon. She cast her ballot in Solesme, north-western France. Both Mr Fillon and his wife have had a colourful campaign to say the least, as our coverage here shows.
Image source, AFPPenelope Fillon votes in Solesme
Image source, ReutersWelcome to the BBC's live coverage of the first round of voting in the French election. We'll be bringing you updates as voters go to the polls to choose their next president.
Eleven candidates are vying to be the country's next leader, with the top candidates spanning the political spectrum from far-left to far-right.
If no candidate wins 50%, the two with the most votes will go into a run-off in a fortnight's time.
Polling stations in France opened at 08:00 local time (06:00 GMT), although some overseas territories began the voting on Saturday. Voting ends at 20:00, with exit polls expected quickly afterwards.