Jean-Luc Melenchon, 60, a former Trotskyist and Socialist minister, is attracting up to a 100,000 people to his rallies for his Front de Gauche -- Left Front. In the Place de la Bastille in Paris, in Toulouse last weekend and in the Marseilles beach Saturday, voters thronged to be thrilled by his passionate rhetoric that condemns the rich and insists that the spirit of the French revolution still burns bright.
From less than 5 percent in the polls in February, Melenchon reached double digits as March began. He hit 15 percent at the beginning of April and 17 percent last week. There are rumors of private polls that have him touching 20 percent.
The latest poll for Le Parisien indicated 60 percent of voters polled say Melenchon is the candidate who most represents change and 28 percent said he had "the stature to be president."
It would be an extraordinary shock were Melenchon to be one of the two leading vote-winners Sunday. The top two would have the right to go forward to the run-off election May 6.
The shock wouldn't be limited to French politics. With his program demanding confiscation of all incomes above $470,000 a year, big increases in the minimum wage and French departure from NATO, success for Melenchon would stun the financial markets and could well trigger a serious new crisis for the euro.
Could it happen? It is unlikely but not impossible. French voters have done this before.
In 2002, they put the extreme right-winger Jean-Marie Le Pen into second place behind the incumbent President Jacques Chirac, and knocking the Socialist Prime Minister Lionel Jospin out of the race. Chirac went on to win in a landslide in the second round and incumbent President Nicolas Sarkozy could probably expect a similar big victory if Melenchon were to be his eventual opponent.
The two-stage process of the presidential election means, a traditional French saying goes, that "in the first round, one votes with the heart and, in the second, one votes with the head." An emotional, even a sentimental vote for the old leftist traditions Sunday could tempt voters to Melenchon in the first round. Young voters, the unemployed and French-born children of immigrants look like voting with greater intensity than usual, which would also favor Melenchon.
Even if he loses, Melenchon could well prove a decisive factor in the second round. A poll for Yahoo! last week indicated 52 percent of respondents favored an alliance between Melenchon and Socialist candidate Francois Hollande in the second round. But the prospect of a left-wing firebrand like Melenchon so close to power could inspire centrists to support Sarkozy.
The latest polls indicate Hollande and Sarkozy each drifting down to 26 or 27 percent of the first-round vote, with Hollande expected to win the run-off by 6-8 percent.
The TV debates before the final vote are likely to be crucial and will probably affected by outside factors like the state of the euro crisis and the reaction of the bond markets.
The euro crisis has put Spain into the spotlight after the yields on its bonds touched the danger level of 6 percent again last week. Markets feared that the new austerity measures by the Madrid government would doom hopes of an early return to growth; they also noted that spending by Spain's semi-independent provincial governments seemed to be running out of control. Spain's banks are sitting on a pile of dubious debts from the housing disaster that left a million apartments unfinished or unsold. And unemployment is running at 24 percent, double the European average.
"Today the problem is solved," Sarkozy declared just five weeks ago. "How happy I am that a solution to the Greek crisis, which has weighed on the economic and financial situation in Europe and the world for months, has been found."
Whether he faces Hollande or Melenchon, those words could come back to haunt Sarkozy in the days before the second round of voting.
In the unlikely event that Melenchon is Sarkozy's second-round opponent, the markets will take fright. But if Hollande is Sarkozy's opponent and goes on to win, the markets will take a hard look at Hollande's own center-left program. It includes a new top tax rate of 75 percent, pushing back the retirement age to 60 and forcing a renegotiation of Europe's new financial stability pact.
Whatever the French voters do Sunday, the euro is in for a rough ride.
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