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.
Citizens in some overseas territories and many French expats abroad have begun voting.
The polls opened in metropolitan France at 08:00 local time (06:00 GMT) on Sunday and close at 19:00 (17:00 GMT).
Polling stations will remain open in some big cities until 20:00 local time (18:00 GMT), with early estimates of the result due to be reported immediately after they close.
The two candidates, who topped a field of 11 presidential hopefuls in the first round election on 23 April, have offered voters starkly different visions of France.
Mr Macron, a liberal centrist, is pro-business and a strong supporter of the European Union (EU), while Ms 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.
Mr Macron is widely expected to win the vote, but analysts have said high abstention rates could damage his chances.
The run-off will be keenly watched across Europe, ahead of elections in Germany and the UK and as Britain negotiates its exit from the EU.The campaign has been marked by its unpredictability, and in a final twist on Friday evening, soon before campaigning officially ended, Mr 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.
Mr 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 been key issues 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.
Ms Le Pen wants the pension age cut to 60 and to “renationalise French debt”, which she argues is largely held by foreigners.
Mr Macron wants to cut 120,000 public-sector jobs, reduce public spending by €60bn (£50bn; $65bn), plough billions into investment and reduce unemployment to below 7%.If voters opt for Mr Macron, they will be backing a candidate who seeks EU reform as well as deeper European integration, in the form of a eurozone budget and eurozone finance ministers.
Ms Le Pen promises quite the opposite. She wants a Europe of nations to replace the EU.
They are similarly divided on other foreign policy issues. Mr Macron opposes any rapprochement with Russia, while Ms 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. Mr Macron, who quit the Socialist government of President Hollande to found his new political movement, has no MPs, and Ms Le Pen has only two.
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.