With between 18% and 20% of the vote, the far-right candidate has beaten the previous record for Front National

In the run up to Sunday's first round presidential vote, it was hard to find many people in France publicly admitting they intended to vote for Marine Le Pen. Nevertheless between 18% and 20% appear to have done so – a stunning result for the far right.

It was a record for France's Front National, beating the previous best in 2002 when Le Pen's father, Jean-Marie, won his way into the second-round run-off with 17% of votes.

The surprise score reflected not only how Marine, a 43-year-old lawyer, made inroads into the French political landscape during a campaign in which she relentlessly challenged the "established" candidates, but also a deep disillusion with the main parties. She has now become the third force in the presidential campaign and a possible kingmaker in the second-round run-off in two weeks's time.

French opinion polls have a record of underestimating support for the far right. Until now, the high point for the Front National, a presence in Gallic politics since the 1970s, was 2002. It was exactly 10 years ago, when Jean-Marie Le Pen, a one-eyed former stormtrooper, caused a political tsunami and found himself voted into the second round of the presidential election.

Everyone had said it could not happen. The opinion polls suggested it would not. It did. In what had been considered an unthinkable result, Le Pen senior knocked the socialist candidate and former prime minister Lionel Jospin out of the race to enter the second round.

He then lost, as voters left and right threw their support behind the centre- right candidate Jacques Chirac (some on the left voting with a clothes peg on their nose to mark their dislike of having to do so), but Le Pen's success caused a national trauma and much soul-searching.

Marine, Jean-Marie's youngest, whom he once recommended to the party as a "big healthy blonde girl ... an ideal physical specimen" , sought to "de-demonise" the party. And in many ways she succeeded in defining the right-wing agenda, forcing Sarkozy to veer to the right in the hope of picking up her votes.

When it came to taking a tough line on immigration and Europe, Le Pen maintained that the French would not be fooled and would prefer the original, ie, her, to the copy, ie, Sarkozy. Her manifesto, with its emphasis on patriotism, protectionism, state regulation and the re-industrialisation of France, played well in the industrial heartlands of the north among the unemployed blue collar workers whose concerns she sought to echo.

Le Pen vowed to pull France out of the euro, to reduce legal immigration to just 10,000 newcomers a year, to scrap the Common Agricultural Policy, leave the passport-free Schengen zone – one of the pillars of European integration – and re-establish old-fashioned discipline, authority and teaching in schools, including fines for the parents of seriously unruly children.

Although Le Pen voters would seem almost certain to vote for the next best right-wing candidate, ie, Nicolas Sarkozy, a poll carried out by BVA before the first-round suggested that while 48% of her supporters would transfer their vote to Sarkozy, 24% would vote for Hollande.

Le Pen's third-place position will have caused deep disappointment in the camp of Jean-Luc Mélenchon who, throughout the campaign, found it hard to conceal his contempt for the Front National president, whom he described as "half demented".

At the beginning of the election campaign, Mélenchon was widely dismissed as a left-wing firebrand with a nice line in incendiary rhetoric. But, as the weeks went by, French voters grew attached to the fiery politician who called for "civic insurrection" and vowed to tax earnings of more than €1m (£820,000) at 100%.

On Sunday, Mélenchon's star reached its zenith, when early results gave him 11.1% of votes, several percentage points lower than had been expected. However, these votes will be vital for Hollande in the second round.

Mélenchon, whose Front de Gauche represented the spectrum left of the Parti Socialiste, including the Communist Party, said before Sunday that there would be no horse-trading with Hollande in the fortnight before the second-round vote on 6 May. Hollande said the same.

Indeed Mélenchon's virulent spade-is-a-spade bombast meant that he described Hollande as being as "useful as the captain of a pedalo in a storm".

Both men, however, are pragmatic and have one overriding common aim now that the electoral field has been reduced to two: to keep Sarkozy from a second term in office.

This shared ambition will need to overcome the suspicions and experience of decades in which France's left has failed to learn that there is strength in unity and defeat in squabbling.

The very reason Jean Marie Le Pen National knocked out the socialist presidential candidate Lionel Jospin in 2002 was because the left fractured.

Mélenchon, a philosophy graduate and former teacher, will be hoping the level of support for his programme will enable him to shoehorn some policies into Hollande's manifesto. Quite where the common ground will be found is anyone's guess; Mélenchon has proposed increased workers' rights and controlling the banks, ideas that Hollande is broadly in favour of, along with dismantling Nato, getting rid of the French diplomatic service and the "absurd free market" and "taking apart all organisations that represent north American hegemony".

If Hollande went to London to reassure the City that he was "not dangerous", Mélenchon has made a point of assuring everyone that when it comes to bankers and their "stinking" money, he would be a genuine menace.

Hollande will have to do some careful juggling in the next fortnight; he needs to swing far enough left to attract Mélenchon's voters but not too far to alienate those nearer the centre, who voted for Francois Bayrou, leader of the Democratic Movement. A poll before Sunday's vote suggested 83% of Mélenchon voters would vote for Hollande in the second round.

François Bayrou must have resigned himself to being the eternal also-ran of French presidential elections, by now. The former education minister, and committed centrist, who will be 62 on Wednesday, polled just 8.5% on Sunday, putting him in fifth place.

It was Bayrou's third presidential election: in 2002 he was in fourth position in the first round, scoring just 6.84% of the votes; in 2007, that score rose to 18.57%.

Like the other left wing candidates, he has proposed raising income tax and VAT, and he supports the introduction of an international financial tax, nicknamed the Tobin Tax, by 2014.

Around 34% of his supporters said would vote for Sarkozy in the second round and 32% for Hollande.