Conservative Nicolas Sarkozy and Socialist Segolene Royal scrambled Monday to claim the sizable centrist vote that went to lawmaker and farmer's son Francois Bayrou, whose strong third-place showing in France's weekend first-round presidential elections made him a potential kingmaker in the May 6 runoff.

With a five-point first-round advantage after Sunday's balloting and a chance to pick up even more of the significant far-right vote he has courted, Sarkozy — a Hungarian immigrant's son who campaigns on national pride and economic reforms — appeared to be in command.

Already two polls suggested that Sarkozy, with his straight talk and tough-love approach to politics, could triumph in two weeks and take the keys to the presidential Elysee Palace, held for 12 years by President Jacques Chirac, 74.

"I want to take charge of suffering," Sarkozy said on a visit Monday to a shelter for women, including illegal immigrants — a clear bid to soften his image after overtly tapping far-right voters.

"A country, for me, is like a family," he said, evoking nurturing themes that are the stock of rival Royal.

Royal, who would be France's first woman president, and Sarkozy, surged ahead of 10 other candidates in Sunday's race, marked by a voter turnout of 83.77 percent — about a point short of 1965's 84.8 percent first-round record.

Definitive results showed Sarkozy with 31.18 percent of Sunday's vote and Royal with 25.87 percent.

Sunday's first-round vote also was marked by a rejection of extreme-right leader Jean-Marie Le Pen who, with 10.44 percent of the vote, received his second-worst score in five tries at the presidency. That was far from his performance in 2002 when voters, in a shock to France, propelled him into the runoff against incumbent Chirac.

But Le Pen's poor score also was a sign of Sarkozy's successful appeal to the extreme-right.

This time, it was centrist candidate Bayrou who surged ahead, gaining 18.57 percent of the vote with his appeal to refound a political system that has pitted left against right since the French Revolution and which Royal and Sarkozy embody.

Just 24 hours after their first-round victories, Royal and Sarkozy planned rallies Monday night with an eye on voters who backed Bayrou, centrist party leader who has used his farm background to put a grass-roots veneer on politics.

"Bayrou has the keys in his hands, we'll have to see what he'll do," said Jean Chiche, an analyst with IFOP, the polling firm.

Royal said she could still win. She said that promised backing from small leftist candidates eliminated in the first round has created a "dynamic," and that their votes together added up to 10-plus percent — a boost that did not eliminate the need for centrists.

"I think it's doable," Royal said.

Both Sarkozy and Royal, a military officer's daughter, are in their 50s and offer France a new generation of politics with no memory of World War II. They also offer voters a clear choice between two ideas of France, a choice that Bayrou opposes in favor of a third way which would see left and right joining in a historic compromise.

The two finalists are to spar in a televised debate, a tradition between rounds — skipped in 2002 when Chirac refused a debate with Le Pen. The proposed May 2 date for this year's faceoff remained unconfirmed. Monday, Chirac laid aside long-standing enmity with Sarkozy to offer him his support.

Bayrou, looking to assure a political future for his newfound popularity — and make it translate into legislative power in June parliamentary elections — planned a news conference Wednesday.

French politics "will never again be the same," he said Sunday night.

Click here to view photos from the first round of elections.

Both Sarkozy and Royal scoffed at Bayrou throughout the months of campaigning, saying he would be incapable of forming a government with ministers drawn from left and right, or gaining a parliamentary majority.

Bayrou's centrist Union for French Democracy has traditionally voted with the right in parliament and has often had ministers in rightist governments. But Bayrou the candidate drew leftist sympathizers to his camp, as well as rightists, and both Sarkozy and Royal need those votes back.

"The door is naturally open," Sarkozy's top lieutenant, Brice Hortefeux, said Monday on France-Inter radio, adding that he felt Sarkozy best embodies the values of the center. But he said that Sarkozy and his governing party, the Union for a Popular Movement, would appeal directly to voters.

Royal's spokesman, Arnaud Montebourg, appealing to Bayrou's voters, argued that the Socialists "exactly" reflect "this project of sustainable political compromise to relaunch France."

The new president faces tough challenges: France is still haunted by 2005 riots by young blacks and Arabs in poor neighborhoods. Decades of stubbornly high unemployment, increasing competition from economies like China's and a sense of diminishing world influence made this a passionate campaign. Royal and Sarkozy have written different recipes to get France back on its feet.

Sarkozy would loosen labor laws and cut taxes to invigorate the sluggish economy. Royal would increase government spending and preserve generous worker protections.

The poor score of Le Pen reflected in part Sarkozy's success in wooing anti-immigrant far-right voters to his camp, a blatant bid made by dangling proposals like creation of a ministry of immigration and national identity.

Two soundings made after Sunday's vote gave the advantage in the runoff to Sarkozy. The CSA poll of 1,005 people gave the conservative candidate 53.5 percent and Royal 46.5 percent. An IFOP poll credited Sarkozy with 54 percent and Royal with 46 percent. In each case, the margin of error, not provided, would be plus or minus three percentage points.