France on Sunday held a second round of voting in local elections that are set to result in a breakthrough by the far right and trigger a reshuffle of the beleaguered Socialist government.

With his party facing a drubbing in the first electoral test since his 2012 election, President Francois Hollande is expected to react by ordering a shakeup of his government. Popular Interior Minister Manuel Valls is tipped to replace current Prime Minister Jean-Marc Ayrault.

The elections will make history with an all-female contest in Paris guaranteeing that a woman will become mayor of the French capital for the first time.

It also looked set to be a landmark vote for the far-right National Front (FN), which is poised to claim a small but significant foothold in France's local government by winning control of as many as a dozen mid-sized towns.

The first indicative results were expected when ballots in metropolitan France close at 8:00 pm (1800 GMT). Indications at midday were that turnout would be low by French standards, increasing the likelihood of the Socialists suffering heavy losses.

That was not good news for Anne Hidalgo, the Socialist candidate for mayor of Paris, as she battled to resist the national swing against her party.

Hidalgo went into the election as the favourite but her rival Nathalie Kosciusko-Morizet, a former minister for the centre-right UMP party, did sufficiently well in the first round to suggest she could edge the contest to join a very small club of women who have run major cities around the world.

The FN's strong first-round performance was widely interpreted as reflecting exasperation among voters with the Hollande government.

The Socialists' failure to get a stagnant French economy moving again and reverse the upward march of unemployment is seen as having aggravated some voters' anger over other issues, such as crime and immigration, and increased disillusionment with mainstream politicians of all stripes.

Ayrault is widely expected to be made the principal scapegoat for the government's failures and Valls, a dapper and tough-talking character who has broad appeal across the political spectrum, is the favourite to replace him.

Hollande's former partner, Segolene Royal, is tipped for a comeback following his separation from girlfriend Valerie Trierweiler in January after revelations of his affair with actress Julie Gayet. Trierweiler reportedly vetoed Royal from being included in Hollande's first cabinet despite the mother of his four children being a long-established Socialist Party heavyweight and former presidential candidate herself.

In the first round, Marine Le Pen's FN took five percent of the nationwide vote -- up from 0.9 percent in the first round of the last municipal polls in 2008 -- despite being able to field candidates only in a minority of municipalities.

Where it did present lists, the FN performed better than expected. It claimed the mayor's seat in Henin-Beaumont in northern France at the first attempt with just over 50 percent of the vote.

Le Pen is hoping to see FN-backed mayors installed in at least another dozen towns on Sunday evening.

The party has controlled a handful of local authorities in the past but does not have a good track record for administrative competence.

Le Pen, who has made strenuous efforts to forge a new, more respectable image for the party founded by her father Jean-Marie, is looking to establish a local base that will allow the party to demonstrate it can be more than an outlet for voters' frustrations.

In an interview with Le Monde this weekend, she said: "What we lack at the moment is a positive report card. That is important. With that we can move to a higher level."

Le Pen, who took over the FN leadership in 2011, has been credited with broadening the appeal of a party regarded as taboo by many voters in light of her father's repeated convictions for Holocaust denial and inciting racial hatred.

The best-known city that could fall to the FN is Avignon, famed for its annual international arts festival, which organisers say will be pulled out if Le Pen's party takes over.