French voters are choosing their next president after an unpredictable campaign that has divided the country.
The second round contest pits centrist Emmanuel Macron, a 39-year-old former investment banker, against the far-right nationalist Marine Le Pen, 48.
The vote is being closely watched across Europe, as the results could affect the future of the EU.
The polls opened in metropolitan France at 08:00 local time on Sunday and close at 19:00.
Polling stations will remain open in some big cities until 20:00 local time, with early estimates of the result due to be reported immediately after they close.
Over 50,000 police officers have been deployed to maintain security.
The two candidates have offered voters starkly different visions of France.
Macron, a liberal centrist, is pro-business and a strong supporter of the European Union, EU, while Le Pen campaigned on a France-first, anti-immigration programme.
She wants France to abandon the euro in the domestic economy, and hold a referendum on France’s EU membership.
Polls suggest Macron will win the vote, but analysts have said high abstention rates could damage his chances.
France is set to elect either its first female leader, or its youngest ever president.
The poll is also unprecedented because neither candidate is from a mainstream political party.
During the first-round of voting, French voters rejected the two big political parties – the Socialists and the Republicans – that have governed for decades.
The run-off will also be keenly watched across Europe, because it comes ahead of elections in Germany and the UK, and as Britain negotiates its exit from the EU.
On Friday evening, soon before campaigning officially ended, Macron’s En Marche political movement said it had been the victim of a “massive” hack, with a trove of documents released online.
The Macron team said real documents were mixed up with fake ones, and electoral authorities warned media and the public that spreading details of the attack would breach strict election rules and could bring criminal charges.
En Marche compared the hack to the leak of Democratic Party emails in last year’s US presidential election that was blamed on Russian hackers.
Macron has previously accused Moscow of targeting him with cyber attacks, which Russia strongly denied.
On Saturday, French President François Hollande promised to “respond” to the attack.
Management of the economy, security, immigration and France’s relationship with the EU have all featured in the campaign.
One of the overriding issues is unemployment, which stands at almost 10% and is the eighth highest among the 28 EU member states. One in four under-25s is unemployed.
The French economy has made a slow recovery from the 2008 financial crisis and both candidates say deep changes are needed.
Le Pen wants the pension age cut to 60 and to “renationalise French debt”, which she argues is largely held by foreigners.
Macron wants to cut 120,000 public-sector jobs, reduce public spending by $65 billion, plough billions into investment and reduce unemployment to below 7%.
On foreign policy, Macron opposes any rapprochement with Russia, while Le Pen met Vladimir Putin in Moscow recently and has previously stated her approval of Russia’s 2014 annexation of Crimea.
The presidential election will be followed by legislative elections on 11 and 18 June.
Whoever wins the presidency will need to perform well in those crucial elections if they want to win a parliamentary majority to push through their proposals.
However, Macron, who quit the Socialist government of President Hollande to found his new political movement, currently has no MPs, while Ms Le Pen has only two.