The French presidential election, the first round of which will be held on April 22, is crucial for the future of the country and the wider European project. Nicolas Sarkozy, who won the presidency handily five years ago promising a "rupture" with France's statist, dirigiste economic model, is fighting for his political life. Odds are he will lose it.

The French electoral system involves two rounds of voting: a first round to winnow the field and a second runoff election between the two leading candidates. All the latest polls give Sarkozy's main rival, the Socialist Francois Hollande, a comfortable 7-10 percent margin of victory in the runoff election, to be held on May 6. Earlier polls also indicated Sarkozy would trail Hollande in the first round. But in the aftermath of Mohammed Merah's murderous attack on a Jewish school in Toulouse and his subsequent killing by the police-which played to Sarkozy's strengths on issues of security, allowing him to assume the role of unifier of a stricken nation-seven out of eight polls released since last Monday placed the sitting president ahead of his opponent by between 1 and 4 percentage points. The battle is far from over.

Its outcome will be determined by the behavior, in the second round, of the voters supporting the other main presidential contenders: doyenne of the far-right Marine Le Pen, whose supporters are more likely to go for Sarkozy in the runoff, the former Socialist senator and current left-wing, anti-establishment firebrand Jean-Luc Melenchon, whose voters will overwhelmingly prefer Hollande, and the popular centrist Francois Bayrou.

Le Pen, daughter of Jean-Marie Le Pen-the xenophobic, Holocaust-denying godfather of the post-war extreme right in France-has done much to soften the rougher edges of the National Front, the party her father founded in 1972. She claims to support restrictions to immigration not because she hates foreigners, but because there aren't enough jobs for French citizens as it is. She maintains that she is not against Islam, only against the "Islamification" of Western society. And she says all this with an easy charm far removed from the aggressive style of her father. Her support in the first round has declined in recent weeks, to between 13-18 percent, but she is still polling better than her father did in the elections of 2002, when he shocked France by coming in second and participating in the run-off against Jacques Chirac.

Bayrou, who shot to national prominence in the 2007 presidential election (he ended up with nearly 19 percent of the vote), is a committed centrist, which in France means liberal on economics and passionately pro-European. He is expected to do worse than in 2007-his numbers have been dipping, down to 10 percent, and he may well finish a disappointing fifth. But assuming this downward trajectory does not continue, his stance on the second round could be the most vital of the three.

Polls show that more than 80 percent of the voters who will plumb for the boisterous Melenchon in the first round will choose Hollande in the second. On the other hand, about half of Le Pen's supporters are saying they will go for Sarkozy on May 6, many motivated by his hardline rhetoric on illegal immigration. If the president hopes to be re-elected, he will need at least half of Bayrou's voters in the second round. This is one of the reasons Sarkozy has refrained from attacking the centrist candidate on the campaign trail, concentrating all his venom on his Socialist adversary instead.

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Hollande lacks the charisma of the last Socialist to be elected president-his namesake Francois Mitterrand, who won his second term in 1988. He has benefited, however, from the deep reservoirs of Gallic distaste both for the reforms imposed on the French economy by globalized capitalism and for their hyperactive but underperforming current head of state.

France has not balanced its budget in nearly four decades and has run a deficit since 2005. It has managed to get through the world economic crisis with less trauma that other major European countries, but its condition today is hardly encouraging: growth is stagnant, unemployment is near double digits, and its big banks are heavily exposed to the debt of troubled eurozone member-states. Its own public debt, at 90 percent, is fast approaching the danger zone.

Faced with all this, Sarkozy has opted for a bout of German discipline. Though he is not personally at ease with German chancellor Angela Merkel, Sarkozy has forged a strong bond with her, supporting Germany's austerity-and-structural-reform-for-all European agenda. His pitch to the French public is that tight budgets and flexible labor markets, along German lines, will boost French competitiveness and renew the economy.

The problem for the French president is that voters seem not to be listening. Aside from the fact that he is personally disliked (his approval rating in March was a dismal 26 percent), the French are none too keen to drink his bitter medicine. His proposal for pension reform, which raises the retirement age from 60 to 62, was extremely unpopular; Hollande is vowing to repeal it, at least in part. The public mood is much more amenable to pledges by the Socialist candidate to increase the tax rate for those earning more than 1 million euros a year to 75 percent and to hire 60,000 teachers.

There's the rub, of course, for Hollande. Like Sarkozy, he is committed to bringing the deficit down to under 3 percent of GDP by 2013, and his policy program is forecasted to balance the budget by 2017. But according to French think tanks that have done the math, his millionaire tax is likely to bring in no more than 200 million euros a year, whereas his new teachers are likely to cost around 1.7 billion euros. In addition, if he is elected, his declared willingness to renegotiate the recently agreed fiscal compact between 25 out of the 27 members of the European Union in order to make it less stringent has already raised hackles in Berlin. If the Eurozone continues to struggle, it may lead to growing unrest in the French bond market. President Hollande will then find, like his illustrious Socialist predecessor did in the early 1980s, that there are rigid limits to the workability of socialism in one country in the context of a German-led and increasingly intertwined European economy.