Premier Michel Rocard resigned Tuesday and was replaced by Edith Cresson, a former Cabinet minister who becomes the first woman to head the French government.

The announcement of the change, widely rumored for more than 24 hours, was made by Hubert Vedrine, spokesman for President Francois Mitterrand.Vedrine said Mitterrand would make a broadcast address to the nation Tuesday evening.

The spokesman gave no reason for the change, and there was no immediate statement from Rocard, who had policy differences with Mitterrand but was not entangled in any specific controversies.

But some media commentators have suggested that both Mitterrand and Rocard would benefit from a change - Mitterrand by putting a fresh face in charge of a government that is bogged down on several political fronts, and Rocard by gaining more freedom to mount a possible campaign for the presidency in 1995.

Mitterrand named Rocard, a longtime political rival, as premier after winning a second seven-year term as president in 1988.

Rocard has survived 11 no-confidence motions introduced in the National Assembly by the conservative opposition. His standing in popularity polls generally has been close to Mitterrand's.

France's president, as head of state, presides over foreign and defense policy. The premier, who is officially the head of government, takes charge of domestic affairs and is held responsible for domestic failures.