The two are to face off on May 6 after Sunday's first round saw Hollande beat Sarkozy by a vote of 28.63 to 27.08 percent, according to near complete official results.
Hollande's victory cemented his position as the clear leader in the race, dealing a blow to right-winger Sarkozy's hopes of gaining enough momentum from a first-round win to defy expectations and return to office.
But it was the shock showing of anti-immigrant, anti-EU flagbearer Marine Le Pen, at 18.01 percent, that shook up the race, setting up her voters as potential kingmakers.
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Hollande told reporters Monday that the vote reflected anger in the country and that he would listen to far-right supporters.
"Nicolas Sarkozy is to blame for the far-right's high level," Hollande told reporters. "There are voters who may have been been led to this through anger. That is what I want to hear."
Polls show the Socialists could attract about a quarter of Le Pen's backers, but it is Sarkozy who will mainly be gunning for their support.
In a speech late Sunday, Sarkozy explained his poor showing as stemming from a "vote of crisis" and brandished his right-wing credentials in a clear nod to Le Pen supporters.
"These anxieties, this suffering, I know them, I understand them," Sarkozy said.
"They are about respecting our borders, the determined fight against job relocation, controlling immigration, putting value on work, on security," he said, hitting on a number of key right-wing themes.
His camp moved quickly Monday to show confidence and seduce far-right voters.
"Hope is strong in our camp, that is what we really think," Foreign Minister Alain Juppe told RTL radio.
"(Sarkozy) is on course to win the presidency... there is no desire for the left today," his former justice minister Rachida Dati told Canal+ television.
She said Le Pen's result "validated the campaign issues" put forward by Sarkozy, including: "controlling immigration" and "strengthening borders".
The first opinion poll after the first round said that Hollande would beat Sarkozy by 54 percent to 46 in the second round.
The two were back on the campaign trail Monday, with Hollande headed to the northern town of Quimper while Sarkozy was to visit the central Indre-et-Loire region to meet farmers and give a speech.
A jubilant Le Pen had addressed her supporters after her National Front party's best ever showing, saying: "The battle of France has just begun."
"Nothing will be as it was before... the people of France have invited themselves to the table of the elite," she said at a remarkably triumphant rally for a candidate who went out at the first hurdle.
Asked how her supporters should vote in the second round, Le Pen said: "I will give my opinion on May 1" -- a week before the second round -- but analysts say it is extremely unlikely she will endorse either candidate.
The left has not won a presidential election in a quarter of a century, but with France mired in low growth and rising joblessness, opinion polls had long predicted Hollande would beat the right-wing incumbent.
Hollande says Sarkozy has trapped France in a downward spiral of austerity and job losses, while Sarkozy says his rival is inexperienced and weak-willed and would spark financial panic through reckless spending pledges.
