In what appears to be the start of a major Soviet diplomatic drive to exploit the fissures in the Atlantic Alliance, it was announced here today that Soviet Foreign Minister Andrei Gromyko will come to France next week.

The visit will be his first to a Western country since the invasion of Afghanistan.

The choice of France seemed to be a recognition of what the Soviet ambassador here yesterday called Moscow's "privileged friendship" with Paris.

Soviet officials said that Gromyko would follow up the Paris trip within two weeks with a visit to West Germany and that early visits are being discussed with Spain, Belgium and others, possibly the Netherlands.

Gromyko's Western travel plans seem to indicate Soviet confidence that headway can be made to turn the tables on Washington's efforts to portray Moscow as a menace to East-West detente.

Statements by Soviet officials have an undertone of "we Europeans" -- both East and West -- against "those Americans."

Soviet Ambassador Stepan Chervonenko noted in a speech here yesterday that only three European members of the Atlantic Alliance had bowed to U.S. pressure to accept unconditionally the stationing on their soil of missiles that could reach Soviet territory. The three are West Germany, Italy, and Britain.

Soviet officials said that Gromyko would not visit Italy because it is "too unstable." The Soviets may simply consider it pointless to try to pressure an Italian government whose large Communist opposition condemns the Soviet invasion of Afghanistan and backs Italy's membership in the Western alliance.

There is also no plan for Gromyko to try to visit Britain, the United State's firmest supporter in Europe, since there would be "no basis for discussion," a Soviet said. But Gromyko does seek to visit Belgium and the Netherlands, the two countries that have agreed to accept the missiles with conditions about timing.

Ambassador Chervonenko said that Moscow is still ready to discuss disarmament in Europe if NATO will officially suspend application of its decision to deploy the missiles. The previous Soviet position had been that there could be no further discussion of Moscow's deployment of its mobile SS20 rocket, which is capable of reaching Western Europe from European Russia.

With some success, especially in France, the Soviets have been arguing that the crisis in detente did not start with their takeover of Afghanistan but with the earlier U.S. insistence on stationing Pershing and Cruise missiles in Europe to counteract the SS20s.

Announcing Gromyko's visit almost offhandedly during parliamentary debate, French Foreign Minister Jean Francois-Poncet sidestepped the symbolic nature of the choice of France to start the Soviet diplomatic counterattack.

He repeated the French demand that the Soviets withdraw from Afghanistan but balanced this with implied criticism of the Carter administration. "France has a clear and realistic policy," he said. "It involves neither bowing before the fait accompli nor participating in the escalation of confrontation. . . . France has two weapons, firmness and dialogue. Both are indispensable."

Francois-Poncet went even further in criticizing President Carter's calls for allied support against Iran. The alliance, the minister said "is not, as far as we know, between a protector and those it protects. The solidarity that unites [France] with the United States . . . cannot dispense it from deciding for itself and at the right time the measures that it considers the most appropriate and efficient."

It is important to maintain the dialogue with the Soviets, Francois-Poncet said, because "France has things to say to the Soviet Union." France is in a better position than any other country to work to reestablish detente, he said.

Moscow already seems to have reaped considerable advantage from the refusal of French President Valery Giscard dEstaing to align himself behind Washington. The French position, in the view of leading U.S. analysts, has provided a cover for West German Chancellor Helmut Schmidt to detach his government's policies from Washington's.

The Soviets are expressing interest in Schmidt's proposal for a moratorium on deploying missiles in Europe. Soviet sources say they expect him to pick up the invitation to visit Moscow in late May or early June.

France is also lending the prestige of Paris as the site for a conference of pro-Soviet Communist parties later the same week of Gromyko's visit.