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PARIS (AP) _ President Jacques Chirac's coalition of mainstream rightist parties appears headed toward winning control of France's parliament following a first-round vote Sunday, exit polls showed.

A conservative victory would be a triumph for Chirac, stymied by five years of power-sharing with the outgoing, Socialist-led parliament.

In a first round with a record low voter turnout, the major polling firms gave the mainstream right, including Chirac's Union for the Presidential Majority, between 43 percent and 44 percent of the nationwide vote.

According to the Sofres polling firm, Chirac's right was projected to have 380-420 seats in a new parliament, and the Socialist-led left 135-175 seats, with only 0-2 seats for the extreme right.

The result places Chirac's coalition in strong position to win the final round next Sunday.

Turnout among France's 41 million voters was estimated at between 62 percent and 65 percent _ a record low for the first round of a legislative race under the Fifth Republic, established in 1958. In the last legislative race in 1997, the participation rate in the first round was 66 percent.

``The sheer number of candidates leaves voters confused. It isn't surprising there is such a high abstention rate,'' said Jean-Louis Maurax, a 61-year-old businessman. Many people also said they were more concerned about France's waning soccer fortunes in the World Cup than about the elections.

Another reason for the apathy is that this is the third national election day since April 21.

Chirac desperately wants a majority to avoid another five-year period of ``cohabitation,'' an unwieldy arrangement between opposite political parties that often results in governmental paralysis.

At least 8,456 candidates were running for the 577-seat National Assembly _ between 14 and 15 per seat _ increasing the risk that an extremist candidate might emerge on top should mainstream candidates split the vote.

Ultra-rightist Jean-Marie Le Pen, who stunned France when he finished ahead of Socialist Prime Minister Lionel Jospin in the first round of the presidential race, is not a candidate for parliament. His party scored about 13 percent, according to the exit polls. It was not clear if it would earn any parliament seats.

But the National Front could siphon votes from the conservative right in second-round races where there is a three-way fight between left, right and ultra-right.

Chirac has ordered rightist candidates not to make alliances with the National Front between rounds in order to win.

The top two finishers, plus any candidate winning votes equal to 12.5 percent or more of the number of registered voters in a district, advance to the second, final round on June 16.

To ward off threats from both sides, the main conservative parties _ Chirac's Rally for the Republic, the Union for French Democracy, and Liberal Democracy _ have formed a broad, center-right party, the Union for the Presidential Majority. The party won its first two seats _ in French Polynesia _ in early voting held last week.

The Socialists have been struggling since Jospin, the former prime minister, quit politics after his humiliating loss to Le Pen on April 21. The left is now fighting for its life on the national political scene.