Projections by the CSA polling agency for broadcaster BFMTV showed that up to 30 of the countries departments, or local government units, could switch control from the centre-left Socialists to the UMP, which is headed by former president Nicolas Sarkozy.
Sarkozy called the results a win for his side.
Most observers have said the elections would serve as an early indication as to how voters felt about the current government of the centre-left Socialists, headed by Francois Hollande.
The next elections are in 2017. Hollande has attempted to focus his administration on fixing the economy, but it is not clear even if his efforts are successful whether they will yield enough gains by then.
Prime Minister Manuel Valls on Sunday acknowledged the gains made by the right and called the results a disappointment for the country’s left-wing, but said he would not let the outcome distract him from the government’s reformist agenda, with a current focus on boosting employment levels.
The first round, a week ago, also saw the centre-right top the poll, with the far-right National Front (FN) of Marine Le Pen coming second. reformist agenda,reformist agenda, Socialists were pushed into third place.
It was not yet clear if the FN won any departements on Sunday.
Turnout was low. At 5 pm (1500 GMT), the Interior Ministry reported that 41.9 per cent of eligible voters had cast ballots. Only 42 per cent turned out the week before.