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.
Voter turnout was 28.2% by 12:00 local time (10:00 GMT), down on that of the past two presidential elections.
The vote is being closely watched across Europe, as the results could affect the future of the EU.
Polling opened at 08:00 local time (06:00 GMT) and the final stations close at 20:00 (18:00 GMT), with early estimates of the result set to be reported immediately after.
More than 50,000 police officers have been deployed to maintain security.
Both candidates have been in the north of France on Sunday, with Mr Macron voting near his home in the seaside resort of Le Touquet, and Ms Le Pen in the working class town of Hénin-Beaumont, a stronghold of her National Front party. Both are due back in Paris later in the day.
If Mr Macron wins, his supporters would celebrate in the courtyard of the Louvre. The area was briefly evacuated on Sunday after a suspect bag was found.
A Le Pen victory would be celebrated at the Chalet du Lac in the Bois de Vincennes, on the eastern edge of the capital.
What is the choice facing voters?
The two candidates have offered voters starkly different visions of France.
Mr Macron, a liberal centrist, is pro-business and a strong supporter of the European Union, 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.
Polls suggest Mr Macron will win the vote, but analysts have said high abstention rates could damage his chances.
By noon the turnout, as reported by the interior ministry, was lower than that of the 2012 elections (30.7%) and the 2007 elections (34.11%) at the same point.
Why is the vote important?
France is set to elect either its first female leader, or its youngest-ever president.
This election also marks a new phase in French politics. For the first time, neither of the main parties – the Socialists and the Republicans – has a candidate in the run-off.
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.
What’s this about a hacking attack?
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.
What are the key issues in the campaign?
Apart from the EU, management of the economy, security and immigration 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.
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%.
Read more: Economic challenges facing next president
On foreign policy, 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.
How much power will the winner have?
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, Mr 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.
The candidates in depth:
You can follow the French election on the BBC News website. Click here for all our latest stories.
We will be running a live page bringing together the latest news, video and analysis, from 14:00 BST (13:00 GMT/15:00 local time in France) on Sunday.
On TV, you can watch a BBC World News Election Special, from 18:30 BST, which will be broadcast on BBC News in the UK and on BBC World News internationally, with Christian Fraser presenting from Paris.
For radio, BBC World Service will broadcast a special extended edition of Newshour from Paris at 18:00 GMT on Sunday.