The central paradox of French politics was confirmed once again on 27 March. In a nationwide vote to select local authorities (the so called conseiller général), the far-right National Front gained 11% of the votes cast, but secured only 0.1% of the seats.

This discrepancy between the National Front's popular strength and its actual representation has been a permanent feature of French politics since Jean-Marie Le Pen established the party 40 years ago. But Le Pen was replaced in January by his no less charismatic daughter, Marine. And, with that change, the fate of the Front may be changing, too.

The Front's scant number of elected officials reflects the strategy pursued by its two main adversaries, the Socialist party and President Nicolas Sarkozy's Union pour un Mouvement Populaire (UMP, formerly the Gaullist party), which have essentially shared all elected posts at the national and local level since the 1980s. In order to preserve their shared domination, they have more or less agreed to a "Republican Front" strategy aimed at excluding the National Front in the second round of all elections.

Thus, in a direct run-off between a Front candidate and a Socialist or UMP candidate, the Socialists and the UMP usually vote for each other. The most striking demonstration of this "Republican" alliance was the 2002 presidential election, when, with Socialist support, Jacques Chirac, the Gaullist incumbent, received 85% of the popular vote in the run-off against Jean-Marie Le Pen.

So far, this "Republican Front" strategy of exclusion has succeeded in keeping the far right out of any significant political office for four decades, but it has never reduced the size of its electoral base. On the contrary, the National Front gains credibility by never having to test its programme in government.

For last Sunday's run-off, however, Sarkozy broke with convention: in races where a Socialist candidate faced off against the National Front, his position was: "No, neither." As a result, UMP voters split between abstaining, supporting the Socialist, and voting for the National Front.

Compared with Chirac's rigid refusal to consider any kind of rapprochement with the Front, Sarkozy's policy is thus a small step towards recognition of the Front's legitimacy. The left has, of course, denounced this move as risking fascism. But, like it or not, the Front is a legal party. It may be xenophobic, but its leaders never denigrate the republic: there may be fascists members within it, but the party plays by the democratic rules.

And, like it or not, the Republican Front may crumble altogether under Marine Le Pen's leadership of the party her father founded. Her father was, above all, an ideologue, a populist Napoleon who would never moderate his vision of a white and Catholic France in need of a moral revival. Thus, he rejected the French revolution and the modern welfare state as much as he opposed Muslim immigration.

Gaullists and Socialists are proud that they never compromised with Jean-Marie Le Pen, but he would not have negotiated with them, anyway. Le Pen's ambition was always to "save" France, not to become minister of tourism.

His daughter, however, has clearly softened the tone. Since Marine Le Pen took the helm, she has proven herself able to combine the National Front's trademark anti-immigration stance, the hardcore of its ideology, with praise for the state and the republic. And she has brought a fresh anti-capitalist tone to the Front's rhetoric – always a crowdpleaser in France.

Marine Le Pen is seeking the same path to power travelled by Italy's Northern League, the Flemish Interest party, Liveable Netherlands, and the Danish People's party, all of which first became "soft" populist parties. As a result of this shift, in the near future Sarkozy's conservatives may have no choice but to ally with the Front. Sarkozy's attempt to co-opt far-right rhetoric on security and immigration has not worked, because, when it comes to national chauvinism, the French prefer its authentic purveyors.

And the French – and voters elsewhere in Europe – vote for far-right parties the most when the far left is weakest. Indeed, the National Front is strongest precisely where the Communist party once was the leading force. Between one-quarter and one-third of continental Europeans feel permanently disenfranchised and are prepared to vote for any "protest" party, whether far right or far left.

The reason is essentially the same throughout Europe: slow economic growth implies few prospects for a better life, while the welfare state has failed to create jobs. The far left indicts capitalism; the far right points the finger of blame at immigrants. The far left would recommend revolution; the far right, ethnic cleansing.

Anti-capitalist revolution was tried in half of Europe in the last century, with dire results. Expulsion of immigrants has not. Given a slow economy, a failed welfare state and uncontrolled immigration – challenges for which no mainstream parties on the right or the left have any coherent proposals – the appeal of the far-right's soft populism will continue to haunt France and Europe.

• Copyright: Project Syndicate, 2011