Defeated first-round candidate Jean-Luc Mélenchon has yet to endorse Emmanuel Macron, as his other rivals have done - prompting comment from political reporters.
Marine Le Pen successfully attracted many younger voters in depressed parts of France, hit by the impact of globalisation, says a leading French journalist and blogger, Anne-Elisabeth Moutet.
Speaking on BBC World TV, she said many of those voters in struggling "rust belt" areas used to vote for the left, including the Communists.
"They are like the Trump and Brexit voters - they feel that globalisation has treated them very badly," she said.
Those younger voters, she pointed out, have little awareness of the earlier history of Ms Le Pen's far-right National Front (FN).
Ms Le Pen's father, Jean-Marie Le Pen, has convictions for Holocaust denial.
- Copyright: Getty Images
Sylvie Goulard, an MEP and adviser to Emmanuel Macron, has been speaking to BBC Radio 4’s Today programme.
Asked if, when things began, she thought Mr Macron would be the top contender at this stage, she said: “to be honest, no.”
“But we had the feeling that something new was absolutely necessary. The parties – the traditional ones – brought us where we are… we needed, desperately, something else.”
“At the beginning, Emmanuel was still at the government, but everyone knew he was not feeling at ease at all, because he could not have the impact he wanted.”
And when asked if the young candidate would really be the reformist he promises to be, she said: "Well, we hope – and I trust him.
“And not only France, but we really want to change Europe. We are at a turning point – after Trump’s election, with Putin, with Erdogan – it’s a global challenge.
“Either we stick to unilateral co-operation of states, or we go back to nationalism that will bring us nowhere.”
Welcome to our live coverage of the French presidential election, a vote which saw the political establishment candidates knocked out.
Two - Emmanuel Macron and Marine Le Pen - will fight the decisive second round on 7 May. The main developments so far:
- Liberal centrist Emmanuel Macron won with 23.9% of the vote, slightly ahead of far-right National Front (FN) leader Marine Le Pen with 21.4%, with nearly all votes counted
- Mr Macron pledged to unite "patriots" behind his agenda to renew French politics and modernise the country, against Ms Le Pen and "the threat of nationalists"
- Conservative former Prime Minister François Fillon was third, with 19.9%, narrowly ahead of far-left contender Jean-Luc Mélenchon on 19.6%
- Turnout was forecast to be high, at nearly 78%
- Opinion polls suggest that Mr Macron can beat Ms Le Pen in the second round by a wide margin
Le Monde speaks of a new split in French society, after Emmanuel Macron and Marine Le Pen defeated the traditional centre-left and centre-right blocks in the election.
An editorial in the left-leaning daily says the first-round result pits pro-EU, pro-business voters - Mr Macron's supporters - against protectionist, nationalist voters hostile to globalisation, who backed Ms Le Pen.
It is different from the old left-right divide. And voting trends in rural areas were also markedly different from the cities, it says.
The backlash against globalisation was reflected in the strong anti-establishment vote.
French TV channel BFMTV's round-up of the French front pages on Monday morning, with all newspapers focusing on the left-right battle ahead in the second round - without either of the traditional political parties, the Republicans or the Socialists.Copyright: BFMTV
With 97% of votes counted, the two front-runners have maintained their shares of the ballot.Copyright: BBC
BBC News, Paris
Emmanuel Macron is pragmatic - he says he wants to create a new kind of politics, breaking down the divisions between the traditional left and right. His manifesto blends liberal economic reforms with left-leaning policies on social issues. He wants to make it easier for companies to hire and fire staff, to lower taxes on businesses and extend the 35-hour week. Mr Macron also wants to extend unemployment benefits to more people, including the self-employed, to make education a top priority and to encourage a shift to renewable energy.
He presents himself as an optimistic and pro-European candidate who wants to push for deeper integration. Political analysts have compared him to former UK Prime Minister Tony Blair but his critics say he's all talk and no policies.
At 39, Emmanuel Macron could become France's youngest president, but whether he could then secure a majority in parliament remains unclear. He has promised to select candidates from outside the political system - half of them women - for parliamentary elections in June.
Jean-Marie Le Pen, the former president of the Front National and Marine Le Pen's father, held an election night gathering at his Montretout estate in Paris's western suburbs.
He told reporters that he was not jealous of his daughter's success.
"Jealous? Me?" he said, according to French news site 20 Minutes.
The value of the euro jumped to a five-month high, following news of Emmanuel Macron's election success.
In Asia, the euro was up 2% to its highest level since mid-November.
Dean Turner, economist at UBS Wealth Management, said: There will be some relief among investors that a mainstream candidate made it through to the second round.As things stand, Macron is on course to be the next French president, so it is likely that we see a recovery in risk appetite toward French and other European markets."
Front National supporters in the south of France watched the election coverage with great anticipation.
Stephane Ravier, mayor of a section of Marseille, was among them, and told the BBC how the party has changed.
BBC News, Paris
France is entering uncharted political water - and it is not because Marine Le Pen is in the final round of the presidential election.
It is because the next head of state is almost certain to be Emmanuel Macron.
Let us remind ourselves how preposterous this state of affairs would have seemed just a few months ago.
Here was a man who, at 39, had the gall to walk out of government - turning his back on his protector, President François Hollande - and set up his own political "movement".
He had no experience of electoral politics. He had no party backing. He had none of the organisational support of the Socialists, the Republicans or even the Front National.
And yet somehow Emmanuel Macron read the zeitgeist. He found an untapped reservoir of support among the young, the disillusioned-but-optimistic, the anti-cynics.
Read Hugh Schofield's full analysis.
Bild's front page sees Emmanuel Macron's lead in the first round as allowing Europe to breathe a sigh of reliefCopyright: Bild
The number of votes counted has reached 91% and Emmanuel Macron's margin of victory is now 23.5% to 22.08%. François Fillon is in third with 19.74% and far-left Jean-Luc Mélenchon on 19.47%.
The French TV projection published hours earlier by Ipsos/Sopros Steria (below) suggested Mr Macron's final margin would be around 2%.Copyright: BBC
The chairman of the foreign relations committee of the Russian Lower House, Konstantin Kosachev, voiced support for Marine Le Pen in a Facebook post. Hope dies last, he says.
BBC News, Paris
At times, Emmanuel Macron’s campaign HQ felt like an extremely polite rave.
During the long wait for the candidate to come and speak, loudspeakers played techno music. Volunteers holding French flags swayed and some chanted “Macron President". Most crammed towards the front to get a better look at their candidate.
Mr Macron himself came on stage to cheers.
But the campaign supporters inside the arena were not his main audience. His victory speech was a pre-presidential address, directed towards the rest of the country that did not vote for him.
He was sober, sombre, and emotional only when he spoke of his wife’s support. After he left, the crowd drifted away. The DJ played Michael Jackson and Earth, Wind & Fire. In the street at night, as I waited to head back into central Paris, I saw no celebrations, no-one honking their car horns. There is still a second round to fight.
- Copyright: AFP
With just over 6% of the vote, Benoît Hamon's score is the worst achieved by a centre-left candidate since 1969.
And like him the Socialist candidate in that year, Gaston Deferre, finished far behind a hard-left candidate - Communist Jacques Duclos - who won 21% in the first round.
The fact that Mr Hamon finished only marginally ahead of Nicolas Dupont-Aignan, a Eurosceptic outsider, is a humiliation for the Socialists who have spent the past five years running the country.
She may have qualified for the second round but Le Monde commentator Olivier Faye warns that her failure to win the first round has complicated the task she faces on 7 May.
He says she may have done better than she did in 2012, when she polled 17.9% of the vote, and better than her father in 2002, but for several years the opinion polls suggested she would win this first round, and she hasn't.
It is the first time since France's presidential system was introduced in 1958 that neither the centre-right nor the socialist left make the second round of a presidential election.
It is also the best-ever score for a far-right party, with more than 7m votes.