With tears in his eyes, French President Valery Giscard d'Estaing appeared on television tonight, for the first time since his defeat 10 days ago, to bid an "au revoir" to the French people.

Upon concluding his address, he rose from his chair and walked with a heavy, slow step, his back to the camera, out of the room in the Elysee Palace. The camera focused for a long moment on his empty chair as the "Marseillaise," the French national anthem, was played for perhaps the last time at the almost funereal pace that Giscard had decreed.

President-elect Francois Mitterrand has let it be known that at the ceremonies Thursday for the transfer of powers he wants the "Marseillaise" back in its more traditional, triumphantly martial tempo.

Looking older than he usually does, the solemn, 55-year-old president made it clear that he considers his political career over.

"I will remain attentive," he said, "to everything concerning the interests of France. . . I will hold myself at the disposal of my country to defend the principles and the ideas that have guided my life and inspired my action for seven years."

At another point, thanking the 14.6 million people who voted for him, he said, "France will continue to need you. Every time that it is necessary, I know that I will be able to count upon you."

Mitterrand is planning a highly symbolic gesture that seems to demonstrate his recognition that he and Gaullist leader Jacques Chirac share an interest in the rapid elimination of Giscard. As if anointing Chirac leader of the loyal opposition, Mitterrand plans on his first day in office to call on the Gaullist leader, who is also the mayor of Paris, at the Paris city hall. Only once before, in the 1950s, has a postwar French president gone to city hall so quickly. President Charles de Gaulle waited almost six months and his successors at least severaldays.

The president-elect is to name his prime minister on Thursday. It is almost certain to be Mayor Pierre Mauroy of Lille, for years the seemingly eternal No. 2 of the Socialist Party. Mitterrand continued to devote most of his time to seeing a procession of Socialist leaders and politicians close to the party, apparently to put the finishing touches on the Cabinet list and to make preparations for the two-round legislative elections after he dissolves the National Assembly.

The elections are expected June 14 and 21, since Giscard has agreed to relinquish power several days earlier than he had originally indicated. He reportedly had hesitated between quitting immediately so he would not have to transfer his powers to Mitterrand and holding on for as long as the constitution would permit, almost until the end of this month.

A compromise was finally reached in which he would remain until this Thursday so he could preside over one last regular Wednesday Cabinet meeting for which he has ordered Prime Minister Raymond Barre to prepare a balance sheet of the state of France both as an answer to Mitterrand's charges that Giscard ran the economy into the ground and as a yardstick for the Socialist president's performance. Giscard gave a foretaste of that tonight, sketching a broad picture of his accomplishments and saying that he was returning intact the institutions he had been entrusted to safeguard.

Giscard also indicated what a serious error he thought the French people had made in electing Mitterrand and expressed deep foreboding.

"The will of the greatest number has chosen a new president," Giscard said. "I wanted the transition to be carried out according to the rules of republican continuity. That is why I will welcome Mr. Francois Mitterrand to the Elysee myself. That will give proof of the respect for democratic principles and the regular functioning of our institutions."

Giscard seemed to hint broadly that he expects France to fall on bad days but that, under his watchful eye, this need not be fatal.

"On this day that marks an end of great hopes for many people," he said, "I know that many of you share my feelings. You should know that a political event is only one link in the chain of our long history."

Then, he concluded: "I wish each of you good luck, good luck from the bottom of my heart, without bitterness toward some and with warm gratitude toward others. My best wishes also go to the man whom the French people have chosen to be the first among them. And, in these difficult times, when evil prowls and strikes in the world, I wish that Providence will watch over France, for its happiness, for its well-being and for its grandeur."

He paused for long seconds. In a low, choked voice, he said, "Au revoir," and he rose to go.