Twelve years ago Jean-Marie Le Pen, the leader of France’s far-right National Front, stunned the French political establishment by bursting through to the final round of the country’s presidential election. Last weekend Marine Le Pen, his daughter and successor, revived memories of that moment with a triumph in the first round of the French municipal elections.

In polls that spelt yet another setback for President François Hollande, the National Front dominated the headlines. Championing strongly anti-EU and anti-immigration policies, it grabbed control of a town hall in France’s industrial north, an unprecedented victory in that part of the country. In six other towns that it contested, the FN won between 28 per cent and 40 per cent of the vote. The party is now well placed to win a string of towns such as Fréjus, Avignon, Béziers and Perpignan in next weekend’s second round.

We should not overdo the alarm. The FN, which contested just 600 municipalities last weekend out of 37,000, is still a long way from being a national force. But it is now establishing roots well beyond the few gritty Mediterranean towns with which it is associated. There is a real chance that Ms Le Pen’s party will come first in May’s European parliament elections. This will allow her to consolidate her claim that the FN is breaking the historic duopoly in French politics of left and right.

Ms Le Pen’s continuing ascent is a profoundly worrying development for France and for Europe. While she has largely detoxified the raw image that the FN had under her father, the party still retains below the surface a strongly racist and anti-immigrant streak. Its economic policies, which focus on abandoning the euro and erecting protectionist barriers, are not remotely credible. Yet the chronic weakness of the two main parties in France – the socialists and the centre-right UMP – has given her every chance to advance.

France’s two main parties have to reverse their misfortunes if they are to stop Ms Le Pen in her tracks. First. there is the task facing Mr Hollande. After an appallingly slow start in the Elysée, he must demonstrate much more clearly that he is getting a grip on his government.

A few weeks ago he announced a volte-face on economic policy, shifting away from a socialist commitment to high tax and spend. He announced a €30bn cut in social charges on employers, while pledging big reductions in France’s mammoth public spending bill. But the government’s talks with social partners over these plans are grinding at a painfully slow pace.

The UMP, meanwhile, is in a shambles. It performed modestly well in the municipal elections on Sunday. But since Nicolas Sarkozy’s defeat in the 2012 presidential election, it has been rent asunder by infighting over the leadership of the party and its policy direction. The UMP needs to bring this endless bout of internecine warfare to a stop.

The implications of Ms Le Pen’s triumph go well beyond France. It is an early herald of the serious gains that extremist parties are poised to make in May’s European elections. One of the main reasons why the FN did so well at the weekend is that the abstention rate was high. This should act as a warning to voters across Europe that they must cast a ballot in the European poll if far-right parties are not to prosper.

But the big implication of these results is for France. Ms Le Pen has made no secret that her goal is to emulate her father and be a credible candidate for the French presidential election in 2017. While many might find the idea abhorrent, a strong performance from Ms Le Pen three years from now is increasingly conceivable. France’s mainstream politicians must stop the rot while they still can.

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