President Reagan and French President Francois Mitterrand began a summit meeting today with expressions of mutual friendship against the historic background of the 1781 Yorktown victory, where the Americans, with vital French assistance, won their war of independence.

For all the two leaders' desires to stress 1781, World War II and other times when France and the United States stood united, however, the summit opened with indications of important differences between the two nations.

Mitterrand spoke gently but criticized the Reagan administration for its reluctance to increase aid to the world's poor nations. He urged the United States to move as soon as possible into strategic arms negotiations with Moscow, and differed with U.S. policy on Central America, the Middle East and the need for a world energy policy.

He warned that the United States must seize the opportunity to negotiate soon with Moscow or risk a deepening "psychological and moral crisis" in Europe where an anti-nuclear pacifist movement has been gaining strength.

Mitterrand's remarks came in an interview on "Issues and Answers" (ABC, WJLA) taped shortly before his departure for the United States.

A senior American official, who asked not to be identified by name, told reporters that "we could describe the Reagan-Mitterrand meeting as an extenuation, continuation and broadening" of the two presidents' relationship, and described French-American differences as slight.

The socialist French president repeatedly praised the spirit and character of the United States. "When they move away from the best part of their own history, that really upsets me," he said at one point, stressing that he intends his criticisms to be friendly ones.

The two presidents met aboard the French warship De Grasse on the York River, near where French Adm. Francois de Grasse and his fleet helped lay siege to 7,000 British troops at Yorktown in the battle that ended the American Revolution.

The Yorktown Battlefield has been the scene of a four-day Bicentennial re-creation with 3,000 citizen-soldiers in uniform and 1,000 costumed camp followers living in the fields to replay the final days of the siege.

Reagan and Mitterrand will review the French and American "troops" Monday just before the reenactment of the surrender of Charles Earl Cornwallis, who had decided that it would have been "wanton and inhuman to sacrifice the lives of this small body of gallant soldiers."

The two presidents were far from the crowds of Bicentennial participants and spectators as they ate lunch aboard the French ship and then adjourned for a business meeting here.

The summit comes just four days before Mitterrand and Reagan meet again with leaders of 20 other nations at Cancun, Mexico, to discuss international development, one of the subjects on which France and the United States are far apart.

Mitterrand said that if Cancun does not bring the rich and poor nations closer together, it would be better not to have such a summit because total failure would risk a disastrous new round of criticism of the industrial world by the poor.

"So each side must take a step forward," Mitterrand said.

He expressed the hope that Cancun will bring progress toward an international energy policy to help poor nations with crippling fuel costs.

Reagan outlined his belief that private investment and free trade are the best paths for developing nations to follow in a speech last Thursday.

Mitterrand spoke particularly forcefully on the growing antiwar movement in Europe, saying that recent developments have heightened Europeans' concerns that their nations are being marked out as a future nuclear battlefield by the superpowers.

If there are no arms negotiations, there will be an arms race bringing an economic war and perhaps a shooting war, he said.

The American official who briefed reporters noted that Mitterrand also had mentioned the need for a balance of forces between the United States and the Soviet Union. "Both leaders agree on the need for the modernization of the medium-range missiles in Europe in the context of the balance," he said.

On the Middle East, Mitterrand lined up against the United States playing the leading role in attempts to make peace, saying that the peace process must be started by the Mideast states themselves.

Mitterrand said that not only the United States, but also "ultimately" the Soviet Union, must be involved in the peace process.

The American official rejected the suggestion from a reporter that the Reagan administration, despite its initial expression of concern, is upset about Mitterrand's inclusion of four communists in his cabinet.

"I think the basic answer to your question is we judge our relationships in highly pragmatic terms and that is in the day-to-day assessment of how our policies, respective policies, impinge one on the other."

He said Franco-American relations have improved since Mitterrand won election over the more conservative Valery Giscard d'Estaing. Overall Franco-American relations are "excellent and getting better," he said.

In a luncheon toast, the French president said he is sure that mutual contact between Reagan and himself, who first met at the Ottawa summit of industrial nations last July, would enable the two men to get over the difficulties that "inevitably exist in political discussions between two men who have come from different horizons and who have reached the same supreme responsibilities."

Mitterrand said he is confident "the areas of agreement would, in fact, always prove far broader, far wider than any possible differences."