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.
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.
ee8G4-9Jb08 hW-jE3JlimwMisleading allegations, rumours and outright lies about voting and fraud are flooding online spaces in…
At least 158 people have died in Spain's worst flooding disaster in generations. On October…
Google has been fined two undecillion (a two followed by 36 zeroes) roubles by a…
Embarking on a home remodel is an exciting journey, promising enhanced comfort, increased property value,…
The US presidential candidates continued to campaign across key swing states on October 20. Footage…
Elon Musk has said he will give away $1 million a day to a registered…