President Francois Mitterrand, in his first news conference since coming to power, called on the French people today to rally around him and create a "national elan" for making his Socialist program the law of the land.

Mitterrand's appeal for support in what he called France's "great task" seemed designed at least in part to respond to increasingly vociferous opposition from French big business and the political right to his nationalization and taxation proposals, which are expected to breeze through parliament's Socialist majority in the coming few weeks.

In an apparent attempt to assuage concern that also has seeped down into the middle classes, Mitterrand pledged that his government will undertake no nationalizations other than those already announced before the parliamentary elections scheduled in five years. In addition, he announced that the government plans no increase in taxes next year beyond those added this year.

But the thrust of his remarks in a 2 1/2-hour performance televised live into French homes was that the Socialist program is going to be enacted despite the protests from the right, and that consequently all France--including businesses -- should get involved.

"Working together and national elan--this is the conviction that every Frenchman and Frenchwoman should have to be part of a great task," he declared. "France has a role to play, for itself, but also in Europe and the world--for Europe and the world. Many peoples on this earth are looking at France. For many of them, it represents a hope."

After a review of his government's actions since taking over four months ago, Mitterrand said: "Of course, much remains to be done. I have the means to do it. Neither the time nor the will is lacking for me to carry out my promises."

With 329 supporters in the 491-member National Assembly, a majority that can be expected to remain for five years, Mitterrand, who has a seven-year mandate of his own, seemed to be underlining to his opponents that they should not count on political changes to save them from the Socialist program.

"I am not here to please everyone," he added later. "The rules of the game are set for a long time, at least until the next legislative elections in five years."

Scheduled for submission to parliament Oct. 8, the nationalization bill calls for the takeover of 36 banks with deposits above a cutoff level of $185 million, in addition to five major industrial firms in chemicals, metal, electronics and glass.

Mitterrand addressed about 400 reporters under eight chandeliers in an ornate ballroom at the Elysee Palace, France's presidential residence. Against a background of baby-blue damask drapery, he spoke from a platform into television cameras across the room, alternating stern looks with hesitant smiles and mildly sarcastic witticisms.

Following a French tradition set by Charles de Gaulle, he took a series of questions at once, one after the other, then gave his response in the form of a short speech designed more to drive home his points than respond to the questions. In contrast to de Gaulle, however, he referred to the questions and answered those he appeared to judge useful.

Reporters had no opportunity to follow up on what was left unsaid. This was not unusual, however, in a country where the office of president commands great respect among journalists as well as the public at large.

On foreign policy, Mitterrand reiterated his position that the Western alliance should strengthen its military capacity to avoid giving the Soviet Union a chance to disrupt the balance of forces. He indirectly endorsed the increased defense spending urged by the Reagan administration, saying it is necessary to prevent a disequilibrium in the mid-1980s.

Mitterrand repeated French support for a Saudi peace plan announced last month that Arab sources here say is meant to replace the new Egyptian-Israeli negotiations on Palestinian autonomy.

The plan, which Crown Prince Fahd of Saudi Arabia urged on Paris during a visit here two weeks ago, calls for recognition of the right of all states in the Middle East to live behind secure borders in return for Israeli withdrawal from all Arab land occupied in the 1967 war.