Polling stations witnessed a leap in support for the Socialists and a new high for the far-right on Sunday.
The Socialist opposition with its Communist and Green party allies won 40.5% of the national vote, against 34% for the ruling coalition led by President Jacques Chirac's Union for a Popular Movement (UMP) party, according to exit polls.
The far-right won more than 17% of the vote - mainly for the National Front (FN) of the veteran Jean-Marie Le Pen, but also with a small score for its rival National Republican Movement (MNR).
Second round showdown
About 42 million voters are choosing assemblies in France's 26 regions - four of them overseas - and replacing half the membership of councils in the country's 100 departments, or counties.
Parties need to achieve 10% of the first-round vote to make it to the runoff on 28 March.
Definitive results in each region will determine the parties' strength going into round two, but most will see a three-way fight between the UMP, the PS and the FN. The far-left could qualify in some regions.
Turnout was higher than expected at an estimated 61%. Opinion polls last week suggested there was little interest in the election and there were fears that as few as one voter in two would bother to turn out.
Prime Minister Jean-Pierre Raffarin said he would "take into account the message" of the elections and he called on the French to "rally together" for round two.
French Economy Minister Francis
Mer (L) may be reshuffled
"In the period we have been through - especially after the end of economic growth - we have had to act with courage and determination to reestablish republican authority and hasten the return of growth."
The government is banking on the hope that the first round of two-round elections is customarily used by French voters to express their discontent and that many of its supporters who failed to turn out on Sunday will do so in a week.
"This is a rejection of the government's policies ... a rejection of their effects in terms of employment, public services, education, research. In short the French wanted to deliver a serious warning," said Socialist party leader Francois Hollande.
"The vote for the National Front is no longer a protest vote but a vote of conviction," said Le Pen's daughter Marine, who is leading the FN's campaign in the Ile de France region around Paris.
A renewed rebuff for the government in the second round leading to the loss of many of the 14 regions that it now holds in metropolitan France would hasten calls for a cabinet reshuffle and even the replacement of Raffarin, commentators said.