Yannick Noah became the first Frenchman in 37 years to win the French Open tennis tournament today with a fine attacking game that overwhelmed defending champion Mats Wilander.

After winning a tie breaker, 7-3, to clinch the match, 6-2, 7-5, 7-6, Noah fell to his knees on the center court of the Roland Garros Stadium and punched his two fists into the air. He then jumped over the net into the arms of his father Zaccherie, a former professional soccer player from the West African state of Cameroon, as the ecstatic crowd chanted his name.

Noah, easily distinguishable by his Bob Marley-style Rastafarian hairdo, wept with emotion before he went up to receive the trophy from Marcel Bernard, who was the last Frenchman to win it, in 1946. It had taken Noah 2 hours 26 minutes to show that athleticism and touch can triumph on the slow clay courts of Paris over the steady virtues of an outstanding base line player like Wilander.

If the match had gone on any longer, it could have been a different story. By the start of the third set, Noah already was suffering from cramps induced, he explained later, not so much by exhaustion as by acute nervousness. Wilander, on the other hand, seemed to be getting into his stride.

The growing tension felt by Noah communicated itself to the crowd and the question on everybody's minds was "can he last?" Each player managed to break the other's serve at the start of the third set. Noah produced a couple of aces to get out of some tricky situations--and Wilander replied with some fine passing shots.

In the 11th game of the set, Noah broke Wilander's serve. Victory at last seemed within his grasp and there was a tremendous roar from the crowd as he went out to serve for the tournament. But Wilander produced two dazzling returns of serve and another well-angled passing shot to level the set at 6-6.

With everything to play for, the two men went into the tie breaker. Wilander managed to save one match point at 2-6, but by this time he seemed to realize he could no longer win. Noah won the tie breaker, 7-3, when Wilander misplayed a forehand.

It was the 23-year-old Frenchman's first Grand Slam final. Now ranked sixth in the world, one place behind Wilander, Noah has enjoyed a meteoric rise over the past year and is considered to be one of the most gifted all-around athletes in professional tennis. He was taught tennis in Cameroon until the age of 11, when he was spotted by Arthur Ashe and given a tennis scholarship in France. He has a wide range of outside interests, including playing in a rock band, playing soccer and riding motorcycles.

At a press conference, Noah said he had consciously prepared himself for winning the entire tournament--not just a few matches.

"I tried to think about each game and winning every point rather than what it would be like if I won the championship. Of course I didn't always succeed. I was very nervous," he acknowledged.

Noah's victory will mean a considerable boost for French tennis. At the start of the tournament, Jimmy Connors replied with a dismissive "no" when asked whether he considered the French players any threat. He may have to revise that assessment after Noah's success and his own defeat in the quarterfinals by Christophe Roger-Vasselin, who ranks 130th in the world.

It remains to be seen whether the French can make the transition from clay to the faster game that is played on hard courts. Noah is going ahead with his plans to take a holiday rather than play at Wimbledon later this month because of his total lack of success so far on grass.

Today's match was, in a way, a story of an intelligent athlete pitted against a preprogrammed machine. If a computer-powered robot could play tennis, his game would probably be something like Wilander's--a seemingly endless series of top-spin drives from different points along the base line.

Unlike John McEnroe, who lost to Wilander in the quarterfinals, Noah seemed to find the error in Wilander's programming. He prowled around the court, muscles coiled up, just waiting for the opportunity to spring. A short ball from Wilander and he was up to the net in a flash.

These aggressive tactics paid off. Not being a machine, Noah made plenty of unforced errors--but he also outsmarted his opponent, who was not programmed to respond to slams and volleys. It was not until the beginning of the third set that Wilander showed any sign of coming up to the net himself. By then it was too late.

Later Wilander acknowledged that he had not been able to find the right response. "With a player like Noah, my main weapon is passing shots. But today they didn't seem to work 100 percent--and that's what brought me down."