The Williamsburg summit has touched off new strains within France's governing coalition of Socialists and Communists.

The Communists, who serve as junior coalition partners to the Socialists, have sharply criticized President Francois Mitterrand for signing the joint declaration on western security. They have also used the summit as a means of distancing themselves from the government's new economic policies and an austerity program that is likely to cut into the living standards of ordinary Frenchmen.

In a television interview today, Communist Party leader George Marchais said he was "surprised" by the Williamsburg statement that commits France to supporting the deployment of U.S. missiles in Western Europe if negotiations in Geneva for the removal of Soviet SS20s fail. He said France could no longer claim not to be concerned by the Geneva talks on the grounds that no U.S. missiles are scheduled for deployment on French soil.

Earlier in the week, the party's ruling Politburo said France risked losing the freedom of action it acquired in 1966 when general Charles de Gaulle withdrew from the military command structure of NATO.

The seven western leaders present at Williamsburg described the security of their countries as "indivisible" despite France's special position and the fact that Japan is not even a member of NATO. The Communist Party has said the effect of this statement is to include Japan within the NATO alliance and give the United States "carte blanche" at the negotiations in Geneva.

French political commentators have suggested that Mitterrand anticipated the hostile reaction of the Communists by letting it be known at Williamsburg that he had serious "reservations" about the draft, which he signed after some modifications. It was the first such statement on security matters ever issued at a western economic summit.

The French Communist Party's criticisms of the Williamsburg statement echo complaints by Moscow that France is revising its traditional independent foreign policy stance and getting "closer to NATOism." But they also have a domestic importance as they come at a time when French Communist leaders are having difficulty persuading rank-and-file activists of the value of the alliance with the Socialists.

During the past few weeks, the Communists seem to have been trying to get the best of both worlds by remaining within the government and at the same time publicly criticizing specific policy decisions. This contrasts with the image of quiet loyalty they sought to project during the first two years of Mitterrand's term in office--and could foreshadow an eventual break.

The Socialists would like the Communists to stay in the government, if only because it helps them to keep the trade unions quiet at a time of economic stress. With only two ministers in the inner Cabinet, the Communists have little influence over really important policy decisions.

Senior Socialist strategists believe that the breaking point for the Communists is still some time away. If and when it comes, the Communists are likely to choose a pretext other than that of national security since quitting over this issue could identify them too closely with Soviet policies.

Marchais used his television interview today to pour scorn on the economic decisions taken at the Williamsburg summit, which he described as meaningless in view of the continued surge of the dollar on foreign-exchange markets.

"The Americans don't attach much importance to the undertakings they have made . . . . We are going to continue to finance the American budget deficit," he declared.

The Communist complaints have stung Socialist leaders into replying in kind. Government spokesmen have suggested that if the Communists want to remain in the coalition, they should make their criticisms in private.