To change the breakfast eating habits of a nation is a formidable task, as Jack Nakache is finding out.

A few months ago, Nakache was assigned the task of tailoring that very American invention -- breakfast-time television -- to the needs and expectations of the French. He and his team of programmers at Antenne 2, one of the three principal state-run television stations in France, commissioned a poll to establish whether the French could be sold on the idea as well.

What they discovered was scarcely encouraging -- even if it confirmed what they already knew. The French are a captive audience at lunch and dinner -- long, leisurely meals eaten as often as not in front of the family TV set in the living room or dining room. But breakfast rarely consists of more than a hastily gulped cup of coffee and possibly a croissant.

"The French don't sit down to breakfast in the way Americans do. They are not immobile for such a long time," complained Nakache.

"We have to attract our viewers at the same time as they are rushing round the house doing other things. To make matters even more complicated," he said, "they rarely go into the room where the TV set is located during the morning. You have to remember that only 15 percent of French homes have more than one television set."

Antenne 2's experiment with a morning TV show represents just part of a controversial upheaval in the communications industry here that experts predict will revolutionize French attitudes toward television over the next few years.

The prospect of a huge increase in viewing hours, combined with a similar expansion in the number of television stations, has already provoked divisions within the government of Socialist President Francois Mitterrand. On one side are ministers who would like to preserve state control over the audio-visual media and on the other are some of the president's own advisers who believe there is political capital to be earned by identifying the Socialist Party with the campaign for "free" television.

Conscious of the possibilities opened up by the new technological horizons, professionals like Nakache are more concerned with the content of the programs. They want to avoid the kinds of mistakes they believe have been committed in the United States and Italy, where there are hundreds of different television stations all broadcasting similar shows.

"In France, none of the media have ever been entirely independent of political parties. Our hope, however, is that the multiplicity of sources of information will help to strike a fair balance," Nakache said.

The producers of Antenne 2's new breakfast television show say they have learned a lesson from what happened in Britain a few years back when morning television was launched there. The independent television station Channel Four spent vast sums trying to clone the American breakfast TV shows with their slick production techniques and big-name presenters. But they lost the battle for the audiences to the staid British Broadcasting Corp. (nicknamed the "Auntie") whose presenters were homey and chatty.

In France, the model chosen by Antenne 2 is radio programs built around a series of carefully structured slots in which different presenters and commentators tend to lecture their listeners in the manner of a schoolmaster.

"The American style is to allow the viewer to listen in on conversations that are taking place in a studio between the hosts of the show and their guests," Nakache said. "We think the French prefer to be addressed directly by the presenter."

The polls commissioned by Antenne 2 showed that the French expect tightly packaged information segments when they wake up in the morning. In an effort to satisfy them, the programmers of Telematin have divided up their schedule into a succession of slots with such titles as "Your House," "Your Money," "Your Children's Education," "Your Potplants," plus the news and the weather. There are also cartoons for the kids and a 10-minute mini-series set in a courtroom aimed at the unemployed and housewives.

The launching of breakfast-time television coincided with increasing speculation here about whether the French government will authorize the setting up of private television stations to compete with the three state-run channels. An estimated 1,700 television transmitters are being stocked in France by companies that want to launch their own stations in anticipation of such a decision.

Questioned about the government's intentions at a reception for journalists, Mitterrand indicated he was in favor of some liberalization of state controls over the media. "The problem is how to organize this new liberty," he said.