A strike at a large automobile plant has provided France's Socialist government with a preview of the social unrest it could face in the fall once its economic austerity measures begin to bite.

The new trouble in the car industry erupted last week when Peugeot, France's largest privately owned company, announced that it intended to lay off approximately 10 percent of its 80,000 workers. Here at Poissy, a sleepy town just outside Paris, the news was greeted by an immediate 24-hour shutdown of the Peugeot plant and threats of more protests later unless the measure is withdrawn.

"No layoffs," chanted the workers, most of whom are unskilled immigrant laborers from North Africa who came to France during the economic boom years of the 1960s, as they demonstrated in front of the management building. Inside, union representatives were being told why Peugeot had to follow the example of Chrysler in the United States and Fiat in Italy to cut back costs sharply in order to compete in world markets.

Activists of the Communist-controlled Confederation Generale du Travail (CGT), the labor union to which a majority of the immigrant workers belong, were distributing tracts in French and Arabic.

"Don't hesitate," read one, "your job and your future are at stake. Nothing is more important."

The Peugeot workers, following the tradition throughout France, will all go on vacation in August. When they come back in September, the time of year known in French simply as la rentree, or the return, tensions could begin to rise.

The government monitored last week's events here closely, not because they were particularly dramatic, but because of the pointers they provide to what will happen after the rentree. Following the collapse of ambitious plans for economic growth, President Francois Mitterrand is engaged in a delicate juggling act. He has to weigh the economic necessity of harsh austerity measures against the likely social strains produced by higher unemployment and lower consumption.

The car industry occupies a central place in the French economy and forms a kind of microcosm of its troubles and its prospects. Once the motor of France's industrial success, it has become a symbol of its declining competitiveness. One in every three French citizens now buys foreign cars against one in four five years ago. During the same period, sales of Peugeot cars abroad have slumped by about 50 percent.

The major reason for Peugeot's present economic problems is the failure to adapt quickly enough to the oil price shocks of the 1970s. Faced with a sagging market, car companies in Japan and West Germany proved much more efficient at cutting costs and designing new models. Today they are reaping the benefit.

While citizens of other West European countries were forced to make sacrifices because of the economic crisis, in France, consumption went on rising throughout the 1970s. But when the Socialists came to power in 1981, they set about fulfilling electoral promises to cut working hours, increase salaries and give workers a fifth week of paid vacation instead of reducing public expenditures.

The result of all this increased purchasing power in the economy was an immediate widening in the foreign trade deficit as France sucked in imports from abroad. As domestic costs rose, French exports became less attractive. Unable to sell its cars, Peugeot was forced to cut production. The plant here turns out 1,200 cars a day now, down from 2,200, and workers are on a four-day week.

To finance the trade deficit, which reached a record $12.2 billion last year, France had to borrow heavily on international financial markets. According to statistics collected by the Organization for Economic Cooperation and Development (OECD), France was the third-largest borrower in the world last year after the United States and Canada.

According to the OECD, gross French borrowing reached $14.6 billion last year--up from $6.7 billion in 1981. The pace has slackened somewhat this year to about $6 billion for the first six months. France's gross foreign debt is estimated by private bankers here at $50 billion.

The international financial community began to lose confidence in the French situation, especially since France was borrowing at such a high rate. In April, after months of saying that nothing was really amiss, the government introduced sweeping austerity measures aimed at halving the trade deficit and bringing inflation down to 8 percent by the end of this year.

These objectives are unlikely to be met. The latest statistics indicate, however, that France is moving in that direction. Inflation is down and the trade balance is improving, despite a strong dollar, which makes imports automatically more expensive.

There is, of course, a price to pay. According to the government's statistics institute, unemployment is likely to rise by at least 150,000 to 2.2 million by the end of this year. At a time when the rest of Europe and North America is coming out of recession, the French are likely to see their living standards decline as economic growth stagnates.

"It's like the Bible says." said Yves Laulan, a leading commercial banker. "After seven fat years come seven lean years. There's no way of avoiding it."

Earlier this month, Mitterrand signaled his return to more orthodox economic thinking in a conversation with a French journalist.

"Let's face it," he was quoted as saying, "we all dreamed a bit in 1981." Publication of his off-the-record remarks in an obscure left-wing Catholic weekly was met by expressions of outrage and halfhearted denials by official spokesmen, but most political commentators regarded the leak as deliberate.

The change of heart has been welcomed by the international banking community. France is still considered a generally good credit risk--not as sound an investment as West Germany but still far ahead of European countries such as Italy and Portugal, not to mention Latin American nations such as Brazil or Mexico. As long as the austerity measures are applied with sufficient energy, no one doubts that France will be able to pay back its debts.

The biggest problem facing the Socialist government is persuading its own working-class electors of the need to make sacrifices. It is hardly a coincidence that Mitterrand's popularity began to dip sharply at the very moment the government performed its U-turn on the economy. According to a Gallup poll published last week, only 28 percent of French citizens are satisfied with his performance as president, the lowest level recorded by any French head of state.

The crisis at Peugeot provides a test case of the government's willpower. If it supports the company's decision to go ahead with the layoffs, it runs a risk of provoking serious industrial unrest among a traditionally volatile section of the work force. It is also expected that such a move would put further strains on relations between the Socialist Party and its junior coalition ally, the Communist Party.

If, on the other hand, the government takes the side of the Peugeot workers, it risks jeopardizing its new economic strategy and further antagonizing the international banking community. It is a painful, if familiar dilemma for a left-wing government.