Socialist President Francois Mitterrand appointed a conservative government headed by Jacques Chirac today, the first such power-sharing experiment in the 28-year history of the French Fifth Republic.

In his first policy declaration as prime minister, Chirac, 53, said his government would press ahead rapidly with a program of economic changes aimed at relaxing state controls imposed by the outgoing Socialist administration. But he also promised to respect the constitutional powers of the left-wing head of state, whose term does not expire until 1988.

The Elysee presidential palace's formal announcement of a change of government was followed minutes later by a bomb explosion, in which two persons were killed and nearly 30 injured, just around the corner at a shopping arcade on the Champs Elysees. Police saw the attack as an escalation in a series of bombings in December and February by a pro-Islamic group that has called for the release of Arab prisoners in French jails.

The new government, which was officially appointed by Mitterrand on Chirac's recommendation, includes a minister for privatization, who will be responsible for returning to private control banks, insurance companies and leading industrial groups nationalized by the Socialist government, as well as part of the state-run broadcast media.

A professional diplomat, Jean-Bernard Raimond, was appointed minister of foreign affairs, a politically sensitive post in view of the president's insistence that he will continue to play an important role in the formulation of foreign policy. Raimond, 60, is currently French ambassador to the Soviet Union and served as a diplomatic adviser to conservative former president Georges Pompidou, which gave him longstanding ties to the right.

The nomination of a new government followed three days of intense political negotiation after the narrow right-wing victory in Sunday's election of a new National Assembly. It marked the beginning of what has become known in France as "cohabitation," a word used to describe the unprecedented sharing of executive power between political opponents.

In his declaration, Chirac acknowledged that the appointment of a government with political opinions opposed to those of the president had created a "new situation" under the Fifth Republic inaugurated by Gen. Charles de Gaulle in 1958. But he said that France could be governed efficiently as long as the separate constitutional powers of both the president and the prime minister were respected.

"The French populace has made its choice. It has elected a new majority to the National Assembly and, by this act, it has approved a new policy for our country," he said, speaking from the Paris city hall, where he holds office as mayor.

An initial test of the effectiveness of "cohabitation" in practice will come Friday when Secretary of State George P. Shultz pays a private visit here. He is expected to hold meetings with Mitterrand and senior members of the new government.

The new government includes representatives of all the principal parties in the new right-wing majority in the assembly, including Chirac's neo-Gaullist Rally for the Republic (RPR) and its principal ally, the Union for French Democracy (UDF). The center-right UDF is itself made up of three smaller parties: the Republican Party, the Center for Social Democrats and the Radical Party.

Under Chirac, the RPR, which continues to invoke the memory of de Gaulle, has shifted away from some of the late president's policies.

A longtime Chirac aide, Edouard Balladur, was appointed to the key post of minister of the economy, finance and privatization, in effect making him deputy prime minister. Balladur, 56, will have overall responsibility for implementing the main elements of the conservative election program, which includes the abolition of wealth tax and price controls in addition to returning nationalized enterprises to private control.

Chirac said that the government would push much of the initial legislation through the assembly by decree, a device that enables it to bypass cumbersome parliamentary procedures but requires the approval of the president. Mitterrand is understood to have agreed to the use of decrees in return for the right of veto over Chirac's initial candidates for the ministers of foreign affairs and defense.

The post of defense minister went to Andre Giraud, 60, a former minister of industry in the last right-wing government of president Valery Giscard d'Estaing. Despite his political activity, Giraud is regarded as a relatively neutral figure who should be able to cooperate with Mitterrand in an area traditionally regarded as "reserved" for the president.

Republican Party leader Francois Leotard, vetoed by Mitterrand as defense minister, was named to a new Ministry of Culture and Communication. At the age of 44, Leotard has emerged as one of the rising stars of French politics but was considered too inexperienced and too partisan by Mitterrand for the defense portfolio.

The 37-member government will hold its first session at the Elysee Palace Saturday, with Mitterrand in the chair. The constitution gives the president the right to preside over Cabinet meetings while stating that it is the government that "decides and directs the policy of the nation."

Of the top 21 ministers in the government, 12 are from Chirac's party, while only seven are from its coalition ally, the UDF. The distribution of seats already has upset some UDF politicians, who have pointed out that, with 127 seats in the 577-seat assembly, their party only has 13 fewer deputies than the RPR.

In his statement, Chirac also pledged to use the procedure of a decree to repeal the controversial system of proportional representation under which Sunday's election was held. Right-wing politicians have argued that they would have won a much more comfortable majority in the assembly if the election had been held under the old system of majority voting in single-seat constituencies.

The new prime minister also promised to strengthen law and order and improve France's international standing in line with campaign promises. He said that his government's main priority was the "economic recovery of France."

Many French commentators believe that "cohabitation" has a good chance of working in the short term, if only because both Mitterrand and Chirac fear the popularity of the leading right-wing candidate for the presidency, former prime minister Raymond Barre. Recent polls have shown that Barre, who is fiercely opposed to any cooperation with Mitterrand, easily would win a presidential election if it were held now.

The Socialist Party strategy is to allow the right to run the country for a couple of years in the hope that it will rapidly run into political and economic difficulties.

Other key members of Chirac's government include the neo-Gaullist leader in the Senate, Charles Pasqua, who was appointed interior minister despite Mitterrand's reported objections, and the leader of the powerful French farmers' union, Francois Guillaume, 55, who was named minister of agriculture.