President Reagan heads for Europe this week on his most ambitious foreign policy venture: a summit to discuss economics with six other heads of government in Versailles, France, followed by one in Bonn that will seek to defuse any notion that the NATO military alliance is in disarray.

One task is to convince the others that America is willing to help bring the world economy out of recession, and there will be a prediction that high U.S. interest rates, which are anathema to European leaders, will come down.

A third element to Reagan's 10-day tour underlies the others, and this is a frank effort to create a more favorable European image of the president.

Some White House aides consider the carefully arranged TV exposure, including live TV sessions with European journalists before Reagan leaves Washington Wednesday, to be just as important as the nuts-and-bolts discussions scheduled for Versailles and Bonn.

At Versailles, Reagan will unveil a major proposal for coordinating economic policy among the nations represented, broadening the surveillance powers of the International Monetary Fund. Preliminary agreement to Reagan's initiative has been secured, it was learned, despite an initial and abrupt rejection of it by British Prime Minister Margaret Thatcher.

But the administration is in for sharp criticism. Moreover, it has been shaken by the debacle in Congress last week where efforts to pass a 1983 budget proved futile. "It will be the most difficult and complex summit yet," Assistant Secretary of State Robert Hormats said in an interview.

One of the talking points Reagan had planned to have was a compromise with Congress for significantly narrowing huge federal deficits over the coming years. That now looks to be impossible, reinforcing European fears that interest rates will continue high.

In addition, Undersecretary of State James L. Buckley failed late last week to secure an understanding with his European counterparts that would eliminate interest rate concessions on credits to the Soviet bloc. The unresolved issue therefore will be tossed directly to the leaders at Versailles.

For these and other reasons, White House aides look more confidently to the selling of Reagan than to concrete results.

"This trip is an excellent opportunity to bring the man, his leadership, his philosophy and views to the European public," White House press aide David R. Gergen said at a recent briefing.

An obviously enthusiastic Gergen said: "Through this series of speeches and interviews before he goes, Reagan has an opportunity to reach an enormous audience in Europe and to bring the message about his presidency and what he is seeking to achieve in foreign policy to Europeans in a way he has never had before."

Reagan will also continue his Saturday radio chats to the U.S. public. Next week's will come from Versailles.

Of all the TV pictures beamed back here, the ones that White House officials are counting on the most will be of Reagan's meeting with the Pope at the Vatican on Monday, June 7.

Public relations types at the White House regard this as "a natural," because every TV clip or story will mention that both leaders were almost victims of assassins, an evocation of heroism that could help the president's popularity ratings more than any accomplishments on the economic or geopolitical front.

Gergen said that Reagan would emphasize two themes in his appearances: allied unity and "peace built on a firm foundation of strong defense." The president tried out those themes briefly in his radio talk yesterday, saying that allied security "requires that we continue to work together as friends and allies" and warning that Soviet aggression "has made it harder for progress in arms control."

What Gergen didn't say but implied is that the White House thinks that Reagan's ability to be charming and convincing on the tube, already demonstrated here, will carry over to Europe, where Reagan has an unflattering image.

Numerous ceremonial features have been worked into the president's schedule, with TV coverage, as much as the event, in mind. In England, between summits, Reagan will not only make a televised speech before the Parliament in London, but also will join Queen Elizabeth II at Windsor Castle for horseback riding.

In Germany, he will address the Bundestag in Bonn, then visit the Berlin Wall, an event certain to be widely covered by both European and American television. There is a bit of anxiety about what the White House calls the "peacenik" movement in Europe: In Bonn, a massive anti-American demonstration is anticipated, protesting Reagan's policies on nuclear weapons and on the need for an arms buildup.

Reagan's tight schedule has begun to worry some of the top White House staff. He is to return here this afternoon from his California holiday for two final days of intensive briefings. Beginning Thursday, when he meets with French President Francois Mitterrand in advance of the opening summit dinner Friday night, his schedule leaves no time for naps. The staff concern is whether the routine will tire the 71-year-old president too much.

The administration made a concerted effort last week to downplay the prospects for great accomplishments at Versailles, pointing out that sharp differences divide the United States and its six major allies on many key economic issues. Moreover, the economic summit, the eighth in a series, comes at a time of stagnation around the world.

Beyond that, East-West issues on the Versailles agenda are highly contentious. The United States is trying to discourage the completion of a second Soviet gas pipeline to Europe and to persuade Europeans, especially France, not to grant credits to the Soviets at subsidized rates.

"Just how much credit do you want to grant to somebody that's as intransigent as the Soviets, and do you want to put yourself in the position of giving so much credit to a debtor that the debtor, in turn, controls the creditor?" Treasury Secretary Donald T. Regan asks rhetorically.

Snaps a French diplomat: "In our view, the credit we give to Russia is in our own interest. It's not Ostpolitik [broadening relations with the East]. It's simply that we need the gas, and they offered to sell it at a good price."

Buckley's effort was designed to secure a promise that any future credits to Eastern countries would be at market, rather than subsidized rates.

Hormats, who headed the White House preparations for the summit, said that trade--among the western countries, as well as between East and West--could be among the most difficult issues.

A major problem, Hormats says, is that record unemployment in a number of countries causes them "to look inward," giving rise to a protectionist threat serious enough to throw the international trading system into question.

The same fears--rising unemployment and economic stagnation--lie behind the European concern about high interest rates. After a presummit swing around Europe, Regan said: "They say that high interest rates are killing them." The explanation is that Europe desperately needs new factories to stimulate growth and jobs--requiring an infusion of investment that won't arrive while interest rates are high.

"They blame our deficits for this, and that's a perception we have to deal with, whether it's correct or not," Regan says.

The president's proposal for economic coordination, or "convergence of policy," through the IMF along with regular meetings of the major industrial nations' finance ministers, had its roots in European complaints about high interest rates and what they consider excessive fluctuations in international currency markets.

In effect, this amounts to a protest over the dollar's strength compared with European currencies. The Europeans blame this pattern on high American interest rates. Some European governments have sought, through a process called "intervention," to manipulate foreign exchange markets and reduce the premium commanded by the American dollar.

They are highly critical of what they assert is a "nonintervention" policy by the United States, as articulated primarily by Treasury Undersecretary Beryl Sprinkel.

Without abandoning the substance of American policy, which is to intervene only to correct wildly "erratic" currency movements, Regan has proposed a study to determine any actual benefits of intervention with the help of the IMF staff.

At the least, regular meetings of finance ministers would provide a consultative process that does not now exist, but Regan indicated at the end of the week that the U.S. proposal was even more significant, looking to actual coordination of long-term economic goals through the IMF.

"Perhaps if we can get more guidance [on economic policy] from the IMF--not to make it an international superagency, but it does have a body of knowledge--we could get a greater converging of policy, and there would be less need or cause for intervention," Regan said. Regan said he believed that "the dollar and franc might move together" through such coordination.

It was learned that when British Prime Minister Thatcher heard of the Regan plan, she exploded: "No one is going to tell me how to run economic policy." But Britain and other nations have been assured that there is no such intention. "Wewouldn't want to have the IMF order us around, in that sense, either," an administration official said.

Japan, in an effort to defuse growing frustration in Europe and the United States over its massive trade surpluses, announced measures last weekend represented as a lowering of trade barriers. The Japanese steps have been welcomed generally, but there is a feeling that pressure must be kept on the number two economic power in the free world to do more.

Among other trade issues is the United States accusation of "dumping" by European steel companies and its argument that Canada discriminates against American investments. The U.S. team wants the heads of state to give a "push" to new rules on investment throughout the world.

"The world trading system is at a crossroads," Hormats said. "We've got to resolve our problems between now and the ministerial meeting of GATT the General Agreement on Tariffs and Trade in November."

France's Mitterrand intends to introduce an initiative on high technology. Other Europeans plan to be on guard against any proposal to concentrate production of different types of equipment in different countries.

The final communique, expected to run much shorter than at the previous seven summits, likely will fuzz over the more divisive issues. The United States and the other six are so far apart on North-South issues, especially American-subsidized aid for the Third World through government development banks, that they have virtually been taken off the agenda.

Nonetheless, the summit does provide an opportuntity for the leaders of seven major industrial nations--the United States, Canada, Great Britain, France, West Germany, Italy and Japan--to meet. Despite the inevitable media circus, quiet and sometimes totally private talk will be possible. At the several lunches and dinners, they will talk about political issues--among them the Falkland Islands, the Middle East, and East-West politics.

Assessing prospects for the NATO session, the White House is banking on European leaders' willingness to focus on Reagan's recent pronouncements, especially his address at Eureka College, that toned down anti-Soviet rhetoric. The Eureka speech raised hopes among some Europeans that a cohesive American foreign policy--one they can live with--is about to emerge.

A highlight of the Bonn meeting will be the ceremonial entry of Spain into NATO, which adds important strength to NATO along the Mediterranean. The Spanish entry makes an interesting counterpoint to the relative unreliability of Soviet allies and the Warsaw pact as shown by the Polish crisis.

Assistant Secretary of State Richard Burt took pains at a White House briefing to deny that a crisis exists in the alliance, a theme that will be repeated in Bonn. But the fact that there has lately been a healing process only serves to underscore that wounds were opened by the administration's earlier flamboyant rhetoric, much of which came from Defense Secretary Caspar W. Weinberger.