"We can enter the second round with confidence and I now call on all French people who put patriotism above partisanship or any special interests to unite and join me," Sarkozy told supporters at a rally in Paris.
Sarkozy will face Hollande in the run-off vote on May 6 after Hollande won between 28 and 29 percent of the vote in the first round to Sarkozy's 25.5 to 27, according to ballot-sample estimates.
In his speech Sarkozy hit on a number of key right-wing themes, clearly seeking to garner support from the estimated 18 to 20 percent of voters who backed far-right candidate Marine Le Pen.
Calling the first round a "vote of crisis," he said: "These anxieties, this suffering, I know them, I understand them."
"They are about respecting our borders, the determined fight against (factory) relocations, controlling immigration, putting value on work, on security," he said.
"I know that in this world that is moving so fast, our compatriots' concern about preserving their way of life is central to this election," Sarkozy said.
He called for the support of "all those who refuse the headlong rush into public spending without any control and who don't want France to suffer the fate of its European neighbours already carried away by the crisis."
Sarkozy also called for three debates to be held before the second round but Hollande refused, saying one would be enough.