By Caroline Wyatt
BBC News, Paris
It was an extraordinary turnout by any standards.
Segolene Royal's supporters believe she still has a chance at the top job
French voters, young and old, queued patiently outside polling stations to have their say, and gathered at impromptu election parties to discuss the results.
Some 85% cast their votes - more than any other French election since 1965.
The spectre of Jean-Marie Le Pen's first round success in 2002 loomed large in people's minds, bringing the French back to the traditional left-right divide and away from the political fringes.
That brought the hardline former interior minister Nicolas Sarkozy a higher-than-expected score of 30%, to the delight of his young fans cheering outside UMP headquarters.
One young woman burst into tears of joy.
But the Socialist Segolene Royal did well too, with 25%, and there was a palpable sense of relief at Socialist HQ after what was seen as a lacklustre campaign.
Mr Le Pen was left grumbling on the sidelines in fourth place, with 11%, though his ideas on patriotism, immigration and French identity all entered the two mainstream campaigns of the Socialists and the UMP, with both left and right seeking - successfully - to appeal to his supporters.
Both Mr Sarkozy and Ms Royal have already started fighting for the extra votes they will need on 6 May, hoping to win over the 18% who cast their vote for the centrist Francois Bayrou.
In the end, his appeal to the political centre and for a new "third way" failed to change the face of French politics.
He is expected to announce on Wednesday which candidate he will support in the second round.
Message of harmony
Nicolas Sarkozy has sought to soften his image and remodel himself as a unifier - to counteract his image as a divisive force in France.
Critics say he is too aggressive and impulsive to be trusted as French leader.
They note in particular his comments during the 2005 riots, when he promised to hose the "rabble" from the streets of the suburbs.
So his message on Sunday was one of harmony: "My dear compatriots, I want only one thing," he said.
"To rally the people of France to a new French dream, a French dream which will be the dream of a fraternal republic, where everyone will find their place, where no-one will be afraid of the other, and where diversity will be experienced not as a threat but as a richness."
The left has said he would destroy the much-loved French social model, making the rich richer and the poor poorer.
His campaign has focused on France's ailing economy and an unemployment rate that has remained stubbornly high at 9% of the workforce.
Republic of respect
For her part, Segolene Royal will be relying on the "anti-Sarkozy" vote, playing on fears over his character and his wish to make the French work longer and harder.
"In two weeks time, France will choose its destiny and its new face," said Ms Royal.
"I appeal to all those men and women who want a republic of respect to triumph in France - because we know there is no freedom without justice, no economic efficiency without social progress.
"On 6 May, there will be a clear choice between two very different paths."
The French indeed have a clear choice.
Many of the young say they are firmly in favour of Mr Sarkozy, believing he is the only candidate able to reform the economy and help France compete.
"He's the only man who can make something happen in France, and who can really change people's minds," said one young supporter as he celebrated on the streets.
"We need to get everybody back to work - the 35 hour week has been a disaster," he added.
Mr Sarkozy enters the second round as the clear favourite, according to the latest opinion polls, which give him 54% support to Ms Royal's 46% ahead of the next run-off.
However, young Socialists believe that she can still beat him.
At party headquarters, one young woman insisted Ms Royal would be the best president for France.
"She will be our first female president, and she can change things. She can still make it - we just have to work hard and rally everyone against Sarkozy."
Socialist MEP Pervenche Beres was also optimistic.
"Most people were saying we wouldn't even be in the second round, so now he have the proof that the French people do want a real debate between two visions of society," she told the BBC.
"This country really needs change, and whatever the results of the second round, there will a change because this is a new generation of politicians.
"If Segolene is elected, France will be proud to wake up with a woman president on 6 May."
UMP former Trade and Industry Minister Christine Lagarde also went on the offensive to defend Mr Sarkozy from the anticipated attacks on his personality, which have ranged from accusations of impulsiveness to aggressiveness.
"Having worked with the man, that reputation is really ill-founded," she insists.
"It's an easy game to point at someone's aggressiveness when it's really only passion. His manifesto is a good one, to take France further and higher, and have people roll up their sleeves and create a new France."
French voters will have the chance to make a direct comparison between the candidates in their first head-to-head debate on French TV on 2 May.
But already, the battle between these two very different visions for the future of France has commenced in earnest, ahead of the final and decisive round on 6 May.