Thanks for following our live coverage of the French presidential election. 

We are ending live coverage now, but you can still keep up with the latest developments on the BBC News website.

To recap: 

The decisive second round of the election, on 7 May, will be between liberal centrist Emmanuel Macron and nationalist leader Marine Le Pen.

Mr Macron, 39, heads a new movement called En Marche! ("On the Move"). He came top, with 23.75%, ahead of Ms Le Pen on 21.53%. He is the clear favourite to become president.

The result showed France deeply divided. Mr Macron stands for an open, free market economy and supports the EU. He dominated the vote in the cities.

Ms Le Pen is protectionist and wants to drastically cut immigration. She polled strongly in rural areas and struggling "rust belt" towns.

The French political system is presidential - so the president really is the country's top politician, wielding actual power.

But the president also has to appoint a prime minister who can command a majority in the 577-seat National Assembly - the lower house of parliament. 

That could be a problem for either Mr Macron or Ms Le Pen, because France holds National Assembly elections in June. The assembly is currently dominated by the Socialists (271 seats) and centre-right Republicans (193). 

The plans of a Macron or Le Pen presidency could come unstuck if French voters do not shake up the political system again in June. 

Image source, AFP

Sunday's vote has shown France to be deeply divided. The shock is that neither of the top two candidates represents the traditional establishment.

So what are the key differences between liberal centrist Emmanuel Macron and his far-right rival Marine Le Pen?

• Mr Macron, a former banker, backs the free market, calling for pro-business measures such as slashing corporation tax from 33.3% to 25%
• Ms Le Pen is anti-globalisation - she vows to protect French jobs, condemning liberal policies that have left many workers struggling 
• Mr Macron believes in the EU and wants reforms to make it more effective
• Ms Le Pen condemns the EU, especially the Schengen open borders system - she wants to quit the euro, restoring the franc, and could offer an in/out referendum on EU membership
• Mr Macron favours open borders, saying immigration is part of what makes a successful economy
• Ms Le Pen wants to suspend immigration, introduce new measures to curb conservative Islam and deport radical Islamists

You can read more about what divides the candidates here.

Image source, AFP

Paris Match news magazine pulls out an interesting fact from the voting - Emmanuel Macron scored significantly better than Marine Le Pen in the big cities, notably Paris, Bordeaux, Lyon and Nantes.

Simon Jack
BBC Business Editor

Macron has been installed as the overwhelming favourite to be the next French president - but what does that mean for business, and Brexit?

For the bigger economic picture, a Macron win removes the chance of a political and economic shock to Europe's core.

Marine Le Pen's calls for France to leave the eurozone have been seen as an existential threat to the entire European project.

Macron's likely win has seen the French stock market and the euro surge as that threat is seen as receding.

Read more: What does French result mean for Brexit?

Margot Cadic is a student from Paris, currently studying in London. She voted for Mr Macron, but worries that "there won't be a huge gap between him and Le Pen" in the second round on 7 May.

"I didn't want Fillon to go through, because Macron has a better chance of beating Marine Le Pen. 

"It's a fascinating time. France will now have to come together and make a coalition," she told the BBC.

Prof Raymond Kuhn, a French politics expert, says the election blow to the centre-right Republicans was largely a rejection of François Fillon, rather than the party itself.

Mr Fillon was hit by allegations that he misused public funds by giving family members "fake" jobs.

"Fillon wasn't too far short of the second round... It was more of a failure of Fillon than of the right," Prof Kuhn told BBC World TV.

 Ms Le Pen "won't have any chance of winning in the second round," he said.

"I think she'll get somewhere in the 30s - she'll get some Fillon supporters and a few Mélenchon [far left] supporters... France is a very divided society."

Image source, EPA

Brian Klaas, a politics researcher at the London School of Economics, tweets:

Nate Silver, the editor of poll analytic website FiveThirtyEight, is rubbishing suggestions in the media that Marine Le Pen could - like Donald Trump and the Vote Leave camp in the Brexit vote - defy all the polls.

Journalists making that kind of remark are "innumerate", he says.

The website has put together a long explanation of the hill that Marine Le Pen faces, titled "Marine Le Pen Is In A Much Deeper Hole Than Trump Ever Was, external".

"There aren’t all that many examples of a 26-point polling error, which is what Le Pen would need", Silver writes - with the caveat that two weeks is a long time in politics. 

This piece of graffiti which "says it all" has notched up several hundred retweets since last night.

It seems to have been scrawled on the monument at Place de la Republique in Paris, and reads:

"Ni patrie ni patron, ni Le Pen ni Macron"

Which translates as:

"Neither fatherland nor boss, neither Le Pen nor Macron" - an apparent reference to the respective nationalist and pro-business attitudes of the candidates.

The poetic rallying cry is being used on Twitter among those who say they will abstain from voting in the second round. 

The campaign is picking up pace again. Marine Le Pen has just lashed out at her rival Emmanuel Macron on the threat from jihadists.

Speaking in Pas de Calais region - a northern stronghold for her National Front (FN) - she said "I'm on the ground to meet the French people to draw their attention to important subjects, including Islamist terrorism, to which the least we can say Mr Macron is weak on".

"Mr Macron has no project to protect the French people in the face of Islamist dangers," Reuters quoted her as saying.

It is a very sensitive issue, after the bloody jihadist attacks that traumatised Paris in 2015, and the shooting of a policeman on the Champs Elysees on Thursday night.

Image source, EPA

Image source, screenshot

French right-wing daily Le Figaro deplores the failure of the centre-right to reach the second round. Ex-Prime Minister François Fillon was "wiped out", it writes.

"The impossible has happened. The right, which has thrashed the Socialists in all elections in the past five years, the right, whose ideas and values have never been so deeply preponderant inside the country, this right whose victory seemed inevitable, was wiped out yesterday," it lamented. 

It remains to be seen how the next president will govern, however, as Mr Fillon's Republicans and the rival Socialists are the biggest groups in parliament.  

So the June parliamentary election could deliver another shock to French politics.

It will be a huge challenge for either Mr Macron or Ms Le Pen to get enough of their candidates elected to parliament.

Liberation, a left-wing daily, says, external Mr Macron is in a position to forge a new centrist, democratic bloc in French politics - neither left nor right.

He could become like a US Democrat president, a commentary in the paper says.

But he was also urged by Barack Obama on Thursday to "fight until the last moment of the campaign", the paper reports.

That appears to be a veiled reference to Hillary Clinton's defeat in the US presidential election despite most observers expecting her to win. 

The left-leaning daily Le Monde warns Emmanuel Macron in an editorial , externalthat he must still work hard to woo the many disillusioned voters.

The vote has been a shock to the French political system, it says, noting that the far-right National Front (FN) got more than 20% of votes for the first time in a presidential election.

Mr Macron also needs to take stock of the degree of social protest reflected in the strong vote for far-left candidate Jean-Luc Mélenchon, Le Monde says.

Eric Maurice, a political analyst at the euobserver website, predicts that , externalthe decisive second round will be a contest between the EU and the far-right. He says it will amount to a referendum.

Mr Macron, unlike Ms Le Pen, is a firm believer in the European project. 

"The prospect of Le Pen being beaten and the wave of anti-EU forces being contained in the bloc’s second biggest country sent sighs of relief in Europe," Maurice writes.

Read our profile of Emmanuel Macron, charting his meteoric rise.  

Image source, AFP

Mr Macron's win in the first round sent European shares surging on Monday and the euro briefly reached five-month peaks, Reuters news agency reports. 

There appears to be market relief that another Brexit-like shock is not on the cards. 

The pan-European STOXX 50 index rose 3%, France's CAC40 almost 4% and bank stocks more than 6%. 

The STOXX Europe 600 index was also up more than 1.6%.

The results map below shows that Mr Macron (pink) dominated regions in the west and part of central France. Ms Le Pen (navy blue) polled strongly in the north-east and south-east.

The map has just been released by the interior ministry.

Today Programme
BBC Radio 4

Jérôme Rivière, a top adviser to Marine Le Pen, tells the BBC that it is now a battle between a pro-EU "open borders" candidate - Mr Macron - and Ms Le Pen, who speaks of restoring French sovereignty.

He told the BBC Radio 4's Today programme: "People are fed up... Macron is not talking about France, but about Europe only.

"We don’t like the EU, we want to gain our sovereignty back... all we have been saying is we want to go back to this Europe of nations."

He said the National Front would "protect our citizens from the massive flow of immigration, from the globalised economy".

"France has been hit very drastically, because of people that took advantage of open borders."

Read a full profile of Ms Le Pen.

After the result of the vote became clear on Sunday night clashes erupted in Paris between "anti-fascist" protesters and police. BFMTV reports 29 arrests, and minor injuries to six police officers and three protesters.

The leftist "anti-fascist" and "anti-capitalist" protesters were opposed to both Mr Macron and Ms Le Pen.

Image source, AFP

The French Interior Ministry has published the first-round results, showing a turnout of 78.69% - that is, 36.4m voters. 

The percentages based on an almost complete count of the vote are:

• Macron - 23.8%
• Le Pen - 21.5%
• Fillon - 19.9%
• Mélenchon - 19.6%