Turnout on Sunday was a record low 46.36 per cent of the 44 million eligible voters.
The Socialists already control 20 of the 22 French regions spread across the mainland and Corsica, along with the four councils in overseas territories, and may now take a clean sweep following the second vote.
The voting is being seen as a key test of Sarkozy's popularity, providing the last major ballot before presidential elections in 2012.
Sunday's results have been viewed as punishment by voters reeling from the global economic crisis that has sent French unemployment soaring to its highest level in a decade.
Jean-Marie Le Pen, the leader of the National Front, appeared jubilant on national television, holding up a poster banned by a court that read "No to Islamism" and declaring that his party's future was bright.
Le Pen's party is now set to take its anti-immigrant message into the second round of the election, where it is campaigning in twelve of the French regions.
There was no public comment from the Elysee presidential palace on the results, but Francois Fillon, the French prime minister, said he was hoping that a better turnout in the second round would help the UMP.
"It is difficult to hold regional elections, mid-term elections in the context of a global financial crisis," Fillon said on the campaign trail in the Paris region on Monday.
The pro-government Le Figaro newspaper said Sarkozy's UMP had "a week to avoid a debacle" by convincing voters who stayed away in the first round to cast their ballots in the runoff.
Speaking to Al Jazeera, Renaud Girard, chief correspondent at the newspaper, said: "People feel that there is no real debate on the political scene in France, that everything is within an elite and that real matters like unemployment, immigration and insecurity are not there to be debated."
The Socialists will now seek to forge alliances ahead of round two and are likely to garner backing from the Europe Ecologie green party, which picked up 12.5 per cent of the vote.
Sarkozy's party faces a continued challenge from the National Front in the next round.
The success of the far-right weakened the UMP's campaign in several regions and allowed the Socialists to pick up votes.
"The National Front was declared beaten, dead, buried by the president," Le Pen said late on Sunday.
"This shows that it is still a national force, and probably destined to become greater and greater."
The vote provided Martine Aubry, the Socialist leader, with a boost to her credibility to lead the deeply divided party, which is set to hold primaries to choose a presidential candidate next year.
However, polls show Dominique Strauss-Kahn, the managing director of the International Monetary Fund and former Socialist finance minister, as the left's best hope of beating Sarkozy.
Nearly three years into his mandate, Sarkozy is struggling with the lowest approval ratings of his presidency and commentators agree he could be beaten in 2012.
The president has sought to downplay the significance of the vote, saying there will be no major government reshuffle even if the 20 members of his cabinet who were on the ballot are defeated.
Sarkozy, 55, was elected on a mandate to turn round France's sluggish economy and bring unemployment down to five per cent, but the worst recession since World War II has forced him to change tack.
Hundreds of thousands of jobs have been lost and Sarkozy has poured billions of dollars in state funds into quick job-creation schemes to try to propel the economy into a full-blown recovery.