French far-right National Front party has made significant gains in local elections, winning an outright majority in Henin-Beaumont on the first round.
The National Front is in first place in some other towns it is targeting, according to projections.
President Francois Hollande’s Socialists have lost ground overall and may lose control of some major towns.
The vote is seen as a key test for the Socialists, deeply unpopular after nearly two years in power.
The Socialists were also hit by the low turnout in the first round of the elections – exit polls suggest up to 35% of voters stayed at home.
The vote is to choose councilors and mayors in more than 36,000 villages, towns and cities.
Marine Le Pen’s National Front party has made significant gains in local elections, winning an outright majority in Henin-Beaumont on the first round
The anti-immigration National Front (FN) took 50.26% of the vote in the northern town of Henin-Beaumont, which has historically voted for the left.
Elsewhere, in Avignon and Perpignan in the south, the party’s candidates for mayor had the biggest number of votes.
In some 200 places FN candidates have won through to the second round next weekend.
Marine Le Pen, National Front leader since 2011, hailed the results, saying her party had “arrived as a major independent force – a political force at both national and local level”.
In most cases, these candidates have little chance of gaining control of the town halls as they will be beaten in round two.
However, it is a big advance for the far right and an expression of the growing popular exasperation with the establishment parties of the right and the left.
Many people who voted for President Francois Hollande two years ago chose to abstain, which has meant losses for the Socialists and in many important towns they will struggle in the second round to hold off challenges from the main centre-right UMP opposition party.
Earlier, pollsters identified half a dozen towns that could see National Front rule as a result of the elections, giving it the chance to show it can be trusted with power after attempts to run four towns in the late 1990s revealed its lack of competence, Reuters news agency said.
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France is voting in a second round of parliamentary elections seen as crucial for President Francois Hollande’s reform agenda.
Socialist Francois Hollande, who was elected last month, is seeking a solid left-wing majority in the lower house.
He has promised to hire more public workers and to refocus EU fiscal efforts from austerity to “growth”.
Socialists and their left-wing allies won 46% in last Sunday’s first round, against 34% for the centre-right UMP.
Nationwide, the turnout was a modest 57%. France’s 46 million eligible voters are picking representatives for 577 seats in the National Assembly.
After the first round, 36 seats out of 577 were declared in constituencies where the winner got more than 50% of the vote. Socialists and their allies won 25 of those seats.
France is voting in a second round of parliamentary elections seen as crucial for President Francois Hollande's reform agenda
The French Senate is already under the control of the Socialists and their allies following elections in 2011.
The Socialist Party has concluded electoral pacts with the smaller Europe Ecology/The Greens (EELV) as well as the Radical Left party – with marginal candidates withdrawing from the second round in order not to split the left-wing vote in individual constituencies.
The vote is also seen as a key test for the anti-immigration National Front (FN), which took 13.6% in the first round.
The FN – which has no nationally elected representative – is hoping to take a number of seats, notably for its leader Marine Le Pen in the northern town of Henin Beaumont.
Another closely watched race will be in La Rochelle in the west. Official Socialist candidate Segolene Royal – who is also Francois Hollande’s former partner – is standing against a dissident left-winger, Olivier Falorni, who defied the national leadership and maintained his candidacy.
In a well-publicized twist in the past week, Francois Hollande’s current partner, Valerie Trierweiler, expressed her support for Olivier Falorni in a tweet.
On the right, the UMP of former President Nicolas Sarkozy has concluded an electoral agreement with its centrist Radical Party and New Centre allies.
The start of Francois Hollande’s term has been dominated by the eurozone crisis. In his month since taking office, he has taken part in a series of summits urging his EU partners to engage in stimulus spending and to consider eurobonds.
His government is due to present a revised budget plan to parliament next month.
