The opposition UMP claims victory and the far right National Front (FN) celebrates further gains.
UMP leader Jean-Francois Cope hailed what he called a “blue wave” of support for his centre-right party.
Marine Le Pen’s FN was heading for victory in up to seven towns, early results indicated.
The Socialists have been hit by growing discontent over the economy.
Turnout in Sunday’s second-round vote was low, which was bad news for President Francois Hollande’s Socialists as it was their supporters who were not voting
The National Front was on course for victory in the southern towns of Beziers and Frejus and in Villers-Cotterets north-east of Paris.
The centre-right UMP appears poised to capture a number of key cities, including Saint-Etienne, Reims and Roubaix.
A reshuffle – and quite likely a replacement for PM Jean-Marc Ayrault – could be announced as early as Monday.
In Paris, which has had a Socialist mayor since 2001, exit polls indicated Socialist candidate Anne Hidalgo was set to defeat UMP candidate Nathalie Kosciusko-Morizet.
It was seen as a consolation for the governing party on a night of setbacks.
Voters were choosing councilors and mayors in more than 36,000 municipalities. FN candidates had won through to the second round in some 200 places.
The FN is widely expected to do well in the European Parliament elections in May – and opinion polls suggest the Eurosceptic party is on course to come top.
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