Socialist President Francois Mitterrand said today he would refuse to sign a government decree to return 65 French companies to private ownership, signaling a trial of political strength with the conservative government headed by Prime Minister Jacques Chirac.

Buoyed by favorable opinion polls and international exposure following trips to New York and Moscow, Mitterrand served notice during France's annual Bastille Day celebrations that he was prepared to use his renewed popularity to raise his first major challenge with the conservatives since they took power four months ago.

Explaining his opposition to the privatization decree in a television interview after reviewing France's armed forces parade down the Champs-Elysees, Mitterrand said he was responsible for protecting the country's heritage and national independence. He said he could not allow national assets to fall into "foreign hands."

The decree is due to be presented to him for ratification at a Cabinet meeting Wednesday.

Mitterrand's statement poses the prospect of an upset in the unprecedented power-sharing arrangement known as cohabitation, which resulted from the right-wing election victory on March 16. While the president has issued general warnings during the past few months about government policy, today was the first time he has objected to a specific decree that is due to receive his signature.

A refusal by Mitterrand to sign the decree on selling off state-owned assets would oblige the government to hold a full-scale parliamentary debate on the measure, which was a key element in the right-wing election program. This could in turn cause political difficulties for Chirac in view of the government's slim three-seat majority in the National Assembly.

Successive French governments have used the decree procedure as a way of pushing controversial legislation through parliament with a minimum of delay. But the decrees need to be countersigned by the president before they can be enacted into law.

A public opinion poll this week in the magazine Paris Match reported that 62 percent of French voters agree that Mitterrand should refuse to support specific decrees if he objects to government policy. The same poll showed a 45- to 27-percent margin in favor of the president's expressing his reservations on the denationalization of large chunks of French industry.

State-owned companies slated for denationalization include banks, insurance companies, armaments manufacturers, the oil company Elf-Acquitaine and a main television channel. The list includes companies nationalized both before and after the Socialists came to power in May 1981.

In the four months since the Socialists lost their parliamentary majority, Mitterrand has concentrated largely on foreign policy, leaving Chirac in charge of the government. He has used his symbolic position as head of state and head of the armed forces to present himself as a guarantor of national unity and as a political referee.

One result of Mitterrand's withdrawal from day-to-day politics has been a sudden surge of his popularity. His standing in the opinion polls, which dipped last year to an all-time low for a French president, now matches the level he achieved during the honeymoon period immediately after his election. Chirac, meanwhile, has begun to lose ground in the polls as his government encounters political difficulty.

The prime minister, who was seated behind the president for the traditional armed forces parade, appeared to be taken by surprise by today's developments. He told reporters that he would have no immediate comment.

Appearing in a relaxed mood during the interview, Mitterrand said he was not seeking to "block everything."

"It is up to parliament to assume its responsibilities," he declared. "If a law is voted that I don't like, I would regret it, but it would still be the law."