Voters sent Nicolas Sarkozy and Ségolène Royal into the run-off for the French presidency yesterday, confounding the hopes of their centrist and far-right challengers in the most closely contested campaign for decades.

Mr Sarkozy, 52, who is promising radical reform to haul France out of stagnation, took 31 per cent of the votes, and Ms Royal, 53, whose unorthodox campaign unsettled many on the Left, won solid endorsement from her own camp with nearly 26 per cent.

François Bayrou, 55, the centrist who had threatened to overtake Ms Royal, earned just over 18 per cent — a strong score for a third candidate but a blow for his attempt to forge a “third-way” revolution in French politics.

The biggest disappointment was suffered by Jean-Marie Le Pen, 78, the veteran National Front leader, who scored only about 11 per cent. This was far below the 17 per cent that took him into the second round in 2002, eliminating the Socialist candidate.

Crowds cheered “Ségo President” outside her constituency home at Melle, in southwestern France, yesterday as her Socialist party, led by François Hollande, her partner, breathed a sigh of relief that she had survived the threat of first-round elimination.

She emerged in her trademark white to greet supporters and promised to bring to France “a democracy where people breathe freely”.

“I will be the guarantor of an impartial state, hostage to no clan, to no pressure group, to no financial powers,” she said.

Her remarks amounted to the launch of her second-round campaign, which will seek to depict Mr Sarkozy as a big-money candidate who stands for the establishment against the interests of ordinary people.

Ramming this home, Mr Hollande said that Ms Royal was the only candidate of change. He also ruled out any pact with Mr Bayrou.

As the unsuccessful candidates from the Far Left called on their voters to support Ms Royal, Mr Sarkozy made his first play for the centrist voters who were deterred by his rightwing rhetoric and backed Mr Bayrou. Eight million people voted for him but it remains unclear which way they will swing in the run-off.

To the cheers of supporters in his Paris headquarters, Mr Sarkozy promised “to rally the French people around a new French dream”.

He would, he said, “protect the French who are afraid, especially the weakest among them . . . from their fears”. This included fending off unfair competition from globalisation, he said.

A record turnout of about 84 per cent reflected the intense interest in a campaign that will see a new, reform-minded generation taking power, five years after President Chirac’s bitter re-election against Jean-Marie Le Pen of the far Right.

Despite an unusually high 30 per cent of undecided voters in the past week, the run-off on May 6 has turned out to be a classical Right-Left duel between champions of France’s two big parties, the Union for a Popular Movement, which Mr Sarkozy took over from President Chirac, and the Socialist Party, which last held the presidency under the late François Mitterrand.

François Fillon, a former cabinet minister who is likely to become Prime Minister under a President Sarkozy, said “democracy is the big winner today because the French people have come back to politics”.

The winner of the run-off will succeed President Chirac, who leaves the Elysée Palace in mid-May after 12 years in office.

The results of various polls released last night suggested that Mr Sarkozy would win the May 6 ballot with between 52 and 54 per cent of the vote against 46 to 48 per cent for Ms Royal.

The path to power

April 22 First-round vote. 12 candidates, seven on left, five on right. To win, a candidate must score more than 50 per cent. Otherwise first two go to run-off

May 6 Run-off. Presidency goes to the one who scores most votes New President appoints a Prime Minister and Cabinet to run the country pending parliamentary elections in June

May 17 President Chirac leaves office for new President. New Prime Minister is installed with new (temporary) government

June 10 First round of general parliamentary elections. Straight majority system (not proportional), but candidates must achieve more than 50 per cent to win seat

June 17 Second round of parliamentary elections to decide seats not won outright in first round

Around June 25 President is likely to reshuffle government after elections. If the new parliamentary majority is from the President’s opposition, it will chose a new Prime Minister who will appoint a government in opposition to the President. No parliamentary election has yet produced such a “cohabitation” after a presidential election, but nothing rules it out

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