Centrist candidate Emmanuel Macron will face far-right leader Marine Le Pen in the decisive second round of the French presidential election next month.
On April 24, results from a full count of ballots in the first round the previous day showed Macron with 23.75 percent of the vote and Le Pen at 21.53 percent, sending them into the May 7 runoff.
Conservative Francois Fillon, a former prime minister, finished third with 19.91 percent, while Jean-Luc Melenchon of the far left came fourth with 19.64 percent.
The latest polls show that Macron would win with 61 percent, over 39 percent for Le Pen, if the runoff were held today. If he wins, Macron, 39, will become France's youngest president ever.
Le Pen quickly launched a salvo against Fillon, accusing him on April 24 of being "weak" in the fight against "Islamist terrorism."
Campaigning at a farmers' market in the small northern town of Rouvroy, Le Pen -- who heads the anti-immigration, anti-Islam National Front -- told reporters that Macron "runs for presidential election while having no program" on counterterrorism issues.
"I'm on the ground to meet the French people to draw their attention to important subjects, including Islamist terrorism to which the least we can say Mr. Macron is weak on," she said.
The first round was held three days after a Paris police officer was killed and two others injured in a shooting attack for which the extremist group Islamic State (IS) claimed responsibility.
Le Pen, who has said she would take France out of the European Union if elected, called the runoff with Macron a referendum on "uncontrolled globalization."
As the candidates looked toward the May 7 showdown, leaders of other EU countries made clear they were pulling for Macron.
German Chancellor Angela Merkel's spokesman, Steffen Seibert, welcomed Macron's success and wished him "all the best for the next two weeks."
"Good that Emmanuel Macron was successful with his course for a strong EU + social market economy," Seibert wrote on Twitter late on April 23.
German Foreign Minister Sigmar Gabriel said it is important for France and for Europe that Macron win the runoff.
Speaking in Amman, Jordan, Gabriel said a Macron victory would signal a "new beginning for Europe," while a win by Marine Le Pen would "push Europe deeper into crisis."
Spanish Foreign Minister Alfonso Dastis also said Madrid hopes a victory for Macron would mark a break in the rise of extremist and populist parties in Europe.
European stock markets surged at the opening, as investors welcomed the result. Macron, a former investment banker who has served as economy minister, has vowed to deepen cooperation across the European Union.
France's CAC 40 index soared 3.9 percent while Germany's DAX rose 2.5 percent early on April 24.
The euro rose strongly on when it began trading on Asian markets overnight, gaining 2 percent against the dollar, but later eased back slightly to be 1.2 percent higher on the day, at $1.08.
Macron praised his supporters for a campaign that "changed the course of our country."
He said he wants to gather "the largest possible" support before the runoff.
He called for hope in Europe instead of fear, a reference to Le Pen's anti-European Union campaign.
"I want to be the president of patriots against the threat of nationalists," Macron told a cheering crowd of supporters late on April 23.
Fillon conceded defeat and urged voters to back Macron, saying Le Pen would bankrupt France if elected.
"There is no other choice but to vote against the far right, I will vote for Emmanuel Macron," Fillon told supporters.
In addition to the future of the EU, the election outcome could have a serious impact on the West's relations with Russia.
Of the top four candidates, Macron was seen as the only one who is a critic of Russian President Vladimir Putin's government.
Observers have said a win for Le Pen or another candidate would be likely to undermine EU unity in keeping up pressure through sanctions and other means.
The April 23 vote was held under tight security following the deadly attack on police.
Authorities said the final turnout figure was expected to exceed 78 percent.