Christian Duxin, tournament director of the French Open tennis championships, shouldn't have a care in the world these days, save the vagaries of the weather in springtime Paris.

His tournament has attained such stature that it is almost obligatory for the best players in the world to participate and most of them do. The championships have become fabulously popular and prosperous by every modern standard, properly regarded alongside Wimbledon and the U.S. Open as the sport's premier events.

But Duxin has this petite probleme: what to do with all the ambassadors who want to come?

"We have only a small place in the stadium for celebrities," he said today, pointing out that the Presidential Tribune in the celebrated 17,000-seat main arena at Stade Roland Garros has a mere 200 seats.

It is here that Philippe Chatrier -- president of the French and International Tennis Federations and the driving force behind the French Open's impressive social climbing of recent years -- entertains VIP guests in high style, with champagne and caviar as they watch frequently gripping tennis passion plays on the red clay below.

"So many people from films, from politics and public life, from business, and from international tennis want to come to Roland Garros now, we have 10 times more demand for places than we can take," Duxin said.

The French has long been regarded as the most important tournament on the continent, but until the past few years -- when France underwent a "tennis boom" comparable to that in the United States in the late '60s and early '70s -- it was not particularly chic or fashionable in fashion-conscious Paris.

Winning used to represent the height of ambition for a few European players who were bred on slow, salmon-colored clay. Their flowing artistic strokes and chessboard tactics were not well-suited to the fast grass courts of Wimbledon and the pre-1975 U.S. Championships, nor to the asphalt-based hard courts, indigenous to America, of which the U.S. Open is now played.

Those surfaces place a premium on speed of hand and aggressive serve-and-volley attack. Grass, with its capricious bounces, also demands an extraordinary athleticism, and a determination to volley the ball before it bounces.

Clay courts, with their more leisurely and higher bounce, require different virtues: patience and stamina to dig all afternoon in the dust, and a proclivity for sliding into shots and working the ball around with ground stokes and finesse to set up a point-ending flourish.

The continentals -- with their repertoire of lobs and drop shots, elegant shotmaking from the back court and clay court temperaments -- considered Roland Garros as their fortnight in the sun. But the rest of the world was largely indifferent, and so, too, was Paris.

Officiating, for instance, was never considered a position of honor in Paris, so it was long left to old men and retired colonels, some of whom fell asleep at their battle posts or read newspapers if the match they were working got boring. Such typically Gallic condescension reinforced the decision of many non-european stars to stay away.

As recently as 1975, only 75,000 spectators attended the tournament over its 14 days. And from 1974 through 1978, the French was desperately concerned about the detrimental competitive effects of World Team Tennis. The now defunct American league kept a number of players, including a handful of name men stars and most of the top women, away from the European clay court circuit.

However, through several years of painstaking organization, slick promotion and image-building, firm commitment to commercial sponsorship and a $7.5 million program to expand and renovate the picturesque grounds and facilities at Roland Garros, the French has been upgraded dramatically -- and with dramatic results.

This year, nine of the top 10 male players filed entries for the French; 17 of the top 20, including the top five: defending champion Bjorn Borg, John McEnroe, Jimmy Connors, 1977 champion Guillermo Vilas and Vitas Gerulaitis.

Martina Navratilova stayed away for vague reasons (presumably, she felt that slow courts are not her bailiwick, and a loss to defender Chris Evert Lloyd could only hurt her professional reputation). Tracy Austin had to go back to Rolling Hills (Calif.) High School for her junior year final exams. But otherwise the women's entry is strong, too.

More than 300,000 spectators are expected to pass through the gates at Roland Garros before the tournament ends on June 8.

Now that the U.S. Open is played on hard courts at Flushing Meadow, N.Y., the French is unquestionably the most important clay court tournament. It forms a kind of trinity with Wimbledon, the supreme test on grass, and Flushing Meadow, which determines the king and queen of hard courts.

Connors' willingness to challenge Borg, Vilas and the other players who grew up on clay on their own beloved courts seemed to get a message across to other players: you can't really call yourself a complete player, an all-court champion, unless you win the French. "I had won just about everything else I wanted to win in the game," Connors said, explaining his decision that Paris had become obligatoire, "but this is the biggest clay court title and a lot of tennis is played on clay."

High on the priority list for the refurbishing at Roland Garros were the locker rooms and player restaurants. No dummies, these Frenchmen. "We try to make more comfortable both the players and the public, because without either one, there is no great tournament," says Duxin.

A new 4,600-seat Court No. 1 -- "our second center court" Duxin calls it -- has opened this year. It is intimate and cozy, with nary a bad seat. The outside courts have been relocated, using land that belonged to the Institut Marey, a research center, which, like the tennis grounds, is owned by the city of Paris. Total seating capacity is now 27,000, 6,000 of it on the eight outside courts, but tickets are limited to 23,000 a day to prevent overcrowding.

Now, if they only had more room for ambassadors.