NOT IN A GENERATION has France had a government so far to the left as the one to be formed now by Francois Mitterrand, the Socialist who won the second and final round of the presidential elections on Sunday. Even if he does not take Communists into his cabinet, he will be under pressure from the Communist Party, whose voters provided his margin of victory. Otherwise he could be severely harassed by Communist opposition either in the National Assembly, for which new elections are to be held within two months, or in the factories.

Mr. Mitterrand, who is 64, does not himself appear to be a doctrinaire man. He was already a familiar, and frustrated, national politicina by the time he joined the Socialist Party, and his views run in the left but reformist and defense-minded part of the French spectrum. In the campaign, he attempted, successfully, to focus the public's attention on the high inflation and painful unemployment remaining underneath the undoubted economic achievements of President Valery Giscard d'Estaing.

President Giscard d'Estaing invited and assisted the Mitterrand challenge by ruling in a style bordering on the imperial. In electing Mr. Mitterrand, French voters set aside that tradition of French leadership for something more self-effacing. The experience of the world's industrial democracies suggests that it takes a high order of personal leadership to surmount the disabilities imposed on an incumbent by inflation and traumatic social change.

Mr. Mitterrand's personal qualities, however, are only part of the equation. The peculiarities of the French electoral system may have no less an effect on the policies he will be in a position to carry out. Mr. Giscard d'Estaing was undone by a decision by many Gaullists to his right to sit out Sunday's second round. Mr. Mitterrand profited by a decision of Communists to his left to neutralize their own miserable showing against him in the first round by climbing on his bandwagon in the second. In his campaign, he put as much distance as he could between himself and the Communists. The way their relationship plays out now is critical.

Mr. Mitterrand's efforts to lead France toward economic growth and social peace will be watched with interest in the United States, whose voters have just chosen a course more akin to that of the government leaving power. Americans will probably watch his guidance of foreign policy with wariness. The United States had become pleasantly accustomed to the Giscard policy, which included an emphasis on strength in defense and in the Third World and allowed for a certain measure of cooperation with Washington. It is hard to predict what Mr. Mitterrand's policy will be. The record of his past views and the tugs of some of his current constituencies are not entirely consistent. His victory adds another element of uncertainty to the task the Reagan administration has set for itself of restoring the strength and unity of the West.