Can French baseball make it to the ooh-la-la league?

When the local Paris soccer club recently played in the European Club Championships here, more than 60,000 fans came to cheer. But this past weekend, when the Paris University Club competed in its European Club Championship, there were more questions than ovations.

''Why do the players wear whose funny caps?'' a puzzled youngster asked his dad.

''It's not a sport,'' one of the few spectators said. ''The players don't even get tired.''

The Paris University Club plays baseball, and the competition was the first baseball tournament ever held here.

On the converted rugby field in the Park des Vincennes, the results left something to be desired. Spain beat Finland 45-0. Sweden topped Denmark 19-2. The French team edged out the Germans 4-2, but even here the quality of play was hardly top-notch.

Balls went through legs and past mitts and bounced over the field in slapstick fashion. Base runners slid when the ball was still in the outfield. Informed statisticians gave up counting the number of errors.

''We only have 3,000 players in France,'' explained Parrick Tugault, president of the French Federation of Baseball and Softball. ''People don't know the game exists.''

Despite this, baseball has a long history here. A group of United States professionals played an exhibition at the 1889 World's Fair in Paris, and Mr. Tugault said the first French team was formed the following year at Lycee Condorcet.

The game gained a degree of popularity in Italy and the Netherlands following World War II. Now 20,000 Italians play regularly. There is even a weekly Italian baseball magazine.

''The GIs popularized the game with them (the Italians),'' Mr. Tugault said, ''but we French didn't take to the Americans. We never accepted American culture.''

In recent years, though, this has changed. The French have gone gaga over such US innovations as fast food, the television series ''Dallas,'' and video games. Combined with an explosion of interest in sports in general - 9 million Frenchmen now belong to an athletic club, according to government figures - Mr. Tugault asks, ''Why not also baseball?''

''If the French knew about the game, I think they would love it,'' he said. ''Within 10 years we could have 100,000 Frenchmen playing. That will take money and a lot of work, but I like to do what's difficult.''

His first success was to play host to the European Club Championship here. He hopes this will stir enough interest in the game to have the Paris authorities construct France's first real baseball field. After that, he wants to bring more US coaches across the Atlantic, and eventually even a professional team to give an exhibition.

''To get people interested, the game has to be shown here on a high level,'' Tugault said. ''Unfortunately, we are not good enough yet to invite an American team.''

The level of French play now is at best that of a poor junior college team. Some of the players picked up the game in the US, but most learned it here.

To manage the club, the French Federation has brought over Martin Stuka, a varsity pitcher from the University of California, Los Angeles. Since two foreigners are permitted on each team, Stuka and a Japanese outfielder, Nori Uchiyama, play for the French. The hope is that the two can carry the team. Against Germany, Stuka struck out 16 men. But he may not be so effective against other teams the French will meet later in the summer during the second part of the tournament.

''The Italians and the Dutch are really good,'' says French team president Olivier Dubaut. ''The Dutch have all these players from the West Indies, and the Italians always have a bunch of Italian-Americans. They send scouts to New York's Little Italy.''

In contrast, Mr. Tugault and Mr. Dubaut admit that the French are quite amateurish. All the players hold full-time jobs during the day, and many are quite new to the game.

To prove the point, a story is told how not so long ago a new team recruit, who asked to remain nameless, came to try out. He had become fascinated with the game during a trip in the US and bought a glove to take back home. He was righthanded. So he bought a glove to put on his right hand. . . .