The State Department said yesterday that the United States will be "watching carefully" the composition of the French government of Socialist Francois Mitterrand, suggesting a U.S. concern that communists might be included.

Spokesman Dean Fischer, while saying "the decision of how France is governed rests with the French alone," justified the statement of U.S. scutiny by saying Washington has "an interest in the composition of the French government, with which we work closely in view of our alliance and our many common interests."

"We will be watching carefully the evolution of events in Franch, particularly the composition of the new government when it is formed," Fischer added. He declined to elaborate.

The State Department statement came as the White House made public a congratulatory telegram sent to Mitterrand by President Reagan. A senior White House official, briefing reporters on the congratulatory message, said the prospect of communists being in the French cabinet "would be something that would attract our attention and cause us to examine the situation carefully."

The White House official added that "we don't feel it is a forgone conclusion" there will be communist participation in a new government.

The French Communist Party supported Mitterrand in the race against incumbent President Valery Giscard d' Estaing, but it is uncertain whether the communists will be given a place in the cabinet in return. French leaders close to Mitterrand indicated that the results of the National Assembly elections expected late in June could decisively affect the makeup of a Mitterrand regime.

"There is obviously an analysis going on of the future course of Franco-American relations" in the light of Mitterrand's victory, the White House official told reporters. He added that "it's anticipated" U.S. relations with France will continue to develop constructively but "we are not drawing any conclusions" other than willingness to work with France at present.

Reagan's congratulatory message, which was sent Sunday, expressed confidence that "the centuries-old tradition of Franco-American friendship," together with shared democratic values, will enable the two countries to meet "serious challenges" to their security and well-being in a spirit of cooperation.