Pollsters said the low voter turnout, estimated at 47 per cent, was likely to penalise Sarkozy's allies in particular, with his supporters lacking the motivation to cast a ballot.
Sarkozy is struggling with the lowest approval ratings since he was elected in 2007.
Sunday's polls are the first held in France since a year-long recession sent unemployment soaring to its highest level in a decade, with nearly three million people now out of a job.
Sarkozy was elected on a mandate to boost France's economy and bring unemployment down to five per cent, but the worst recession since World War II has driven it up to double figures.
Social tensions are also being felt. The government's public debate on "national identity" has raised racial sensitivities and been widely criticised as a divisive project that stigmatises immigrants.
"Turnout was quite low ... which means their is a kind of delusion of the French people with politics"
Le Figaro correspondent
Renaud Girard, chief correspondent for the French newspaper Le Figaro, said the UMP was doing "quite badly" in the polls for two reasons.
"Turnout was quite low, below 50 per cent, which means their is a kind of disillusion of the French people with politics," he told Al Jazeera on Sunday.
"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 second [reason] is that the Socialist party is much ahead of UMP, which is contrary to the presidential election where Sarkozy was leading quite far away from the Socialist candidate."
The Socialists already control 20 of the 22 French regions spread across the mainland and Corsica, along with the four councils in overseas territories.
Frederic Dabi, a director at the IFOP polling agency, predicted a heavy defeat for the UMP.
"The balance of power is extremely favourable for the left," he said.
"It's a regional election, but on March 21 [the second round of the regional votes], we will already be taking that turn towards the  presidential campaign."
Sunday night's projections suggested the far-right National Front of Jean-Marie Le Pen, now running in what may be his last election, had performed better than expected, getting 11 or 12 per cent of the votes.
The National Front played that kingmaker role in past elections, but has lost steam in recent years.