Thirteen months after taking office, the French Socialist government is in trouble. President Francois Mitterrand has had to accept the second devaluation of the franc in eight months and install an austerity program involving higher taxes, reduced spending, and a four-month wage-price freeze.

"It shows how hard it is to expand in a world of slow growth," observed C. Fred Bergsten, former assistant secretary of Treasury, and now head of the Institute of International Economics in Washington.

Mitterrand came into office after a bitter political campaign in which he promised that if elected, he would give top priority to creating jobs and increasing social benefits, including a sharp boost in minimum wages. He kept his word on that, as well as a commitment to further nationalize French industry and banking.

The result has been a sharp increase in inflation, and a worsening of the competitive position of French industry vis-a-vis that of West Germany, France's major trading partner. The French inflation rate soared to 14 percent--worst in Europe except for Italy--while Germany held its inflation rate to less than 5 percent.

The latest devaluation against the West German mark is 10 percent, an adjustment that many financial analysts are saying doesn't go deep enough. Reflecting a general view, the Paris daily newspaper Le Monde says that "the countdown for the next franc devaluation has already started."

Interestingly enough, the weak French franc triggered a perceptible shift in American intervention policy. Last Monday, Treasury Secretary Donald T. Regan ordered the Federal Reserve to enter the exchange markets to slow the slide of the franc (and the Italian lira, which had moved with the French currency). It was the first such currency-propping measure by the United States since the assassination attempt in March, 1981, against President Reagan.

But there is no open-ended or massive American intervention policy that Mitterrand can count on. The intervention was small, more a gesture of good will ordered by Regan to demonstrate that the United States honors a Versailles summit commitment to "work for greater stability" of the world monetary system.

A stronger French franc can result only from a change in the basic situation in France, and that is going to be tricky. Mitterrand makes no secret of where his heart is. He told reporters in Versailles on June 5--just a week before the second devaluation--that he hadn't pursued as rigorous an anti-inflation policy as other major countries "because I do not wish an anti-inflationary jolt brutally to cause unemployment."

Until now, in other words, Mitterrand has been willing to gamble that a Keynesian approach would boost real economic growth--and hence, create jobs--without causing so much extra inflation as to unsettle international financial markets. What he didn't count on was the extent to which the French and German economies would diverge.

According to the International Monetary Fund, not only did prices scoot up more quickly in France than in Germany, but France's deficit on international accounts, covering trade and services, remained around $8 billion this year, the same as last year, while the Germans were swinging from a deficit of that much to an estimated surplus of $4 billion. These effects have been very visible inside France. Increasingly, for example, the Germans took a larger share of the French auto market.

Another unsettling factor is Mitterrand's nationalization policy. American visitors to France who can recall getting barely four francs to the dollar only four or five years ago can appreciate what's happened in the past year. That 25-cent franc, down to about 19 cents when Mitterrand came in, is now worth less than 15 cents (at nearly seven to the dollar).

The big unknown now is the extent to which Mitterrand, in fact, will be able stick to his ambitious political program to rejuvenate the French economy by old-fashioned pump-priming. The austerity program announced at last week's end already dilutes it somewhat. To a large degree, Mitterrand's policy will be shaped by the willingness of the Communist labor unions of the Confederation Generale du Travail to go along with a slower pace on social gains.

France's economic troubles help explain some of the tensions that have existed between the Quai d'Orsay and Washington over the past several months. The highly publicized French demand for "coordination" of economic and monetary policy in effect was a plea for the United States and the rest of the major nations to join France in its reflationary effort--a demand that fell on deaf ears.

And French rejection of American demands for curbing export subsidies to the Soviet bloc was less a matter of ideology than the perceived need to keep the business. All told, about 25 percent of French exports are financed by subsidized loans to the Soviet bloc and to the Third World. True, there is a European ideological objection to Reagan's effort to declare economic war against the Soviets, but that is led by Germany, not France. The French are looking to their pocketbooks.