After some early stumbles, President Reagan recovered in the final half of his European odyssey and largely accomplished his major political goal of reassuring the nations he visited that he is not the sort of man who would lead the western alliance into war.

But, in the manner of his 1980 presidential campaign, Reagan managed to raise doubts about his capacities and mastery of detail among those who saw him close up. He also reinforced his image with the huge U.S. press entourage of an isolated president, surrounded by a cocoon of advisers who are afraid to let him loose in public lest he reveal ignorance about some of his administration's policies.

For all his problems, Reagan appeared to have succeeded in taking the international offensive on the peace issue--the central political purpose of his 10-day trip to France, Italy, Britain and Germany. Over and over again, even as he expressed his loathing of Soviet communism, Reagan offered to negotiate with the Russians on reductions of nuclear arms.

On his final day in Europe, the president underscored this theme by issuing a carefully worded proposal to exchange missile launch information with the Soviets and improve the Washington-Moscow hotline. This proposal contained some items that have been considered before, but effectively continued the negotiating theme that Reagan had established two days earlier in his speech to the Bundestag.

"Remarkable was the understanding President Reagan showed in his speech for public demonstrations of concern about the danger of nuclear war and about the increasing arms arsenals . . . ," editorialized the leading German conservative newspaper, Die Welt.

The General Anzeiser in Bonn commented: "President Reagan's pledge to freedom and peace, disarmament and arms control, was unequivocal and leaves even critics no room for doubt. Never before has Reagan urged real disarmament negotiations with such clarity . . . ."

Assessing the German visit, the Washington Post's correspondent in Bonn, Bradley Graham, reported: "Overall, Reagan was a clear hit in West Germany. His speeches both in the Bundestag and in Berlin had very positive echoes here. Not only did he say the right things, he said them, as Die Welt observed, in the right way." Nonetheless, the demonstrations in Bonn and Berlin showed that an active and outspoken minority continue to doubt the president's intentions.

Reagan's performance in Germany was clearly the most successful part of a trip that started shakily and improved as it went along.

The economic summit in Versailles, where Reagan won very little in concessions on East-West trade, raised the most questions about his performance.

The Socialist newspaper Le Matin observed that Reagan seemed always to be protected and insulated, an observation that became especially pertinent after Reagan turned out to be the only one of the seven world leaders at this summit who refused to meet with the press afterward.

The excuses given by White House aides were unconvincing both to U.S. and foreign reporters. Last year at Ottawa, White House officials explained that Reagan was unavailable because it was his first economic summit and he needed more time to master issues. This year, the same officials tried to use the Ottawa summit as a precedent and expressed surprise that any correspondent expected Reagan to subject himself to questioning.

Clearly, however, the president's advisers calculated that the risks of exposing Reagan were greater than the dangers of the press reporting that he was isolated. The president gave no interviews along the way, and requests for them were denied or ignored. Reporters traveling with him saw Reagan only at formal speeches, or on television. On the few occasions that a member of the traveling press pool was able to ask Reagan a question, the president proved either unresponsive or uninformed.

Administration officials--especially Secretary of State Alexander M. Haig Jr.--drew attention to Reagan's dependence on his advisers by continually describing in the most glowing terms the president's role in the closed summit meeting in Versailles and the equally closed NATO summit in Bonn. Reagan, it was said, played a "commanding" or "important" or "most significant" role. But when these officials were asked to quote something that Reagan had actually said in the meetings, they usually had no response.

The one occasion when Reagan was quoted by an administration official was at Bonn, where a summary of his comments to the other NATO leaders was made available to U.S. reporters. The summary had the ring of truth to it, for it quoted Reagan as using phrases critical of the Soviets and detente, which he has been expressing for at least a decade.

But the speech did not demonstrate that Reagan was particularly effective at close quarters. Even by the U.S. account, Reagan's stump speech was greeted by silence from the other NATO leaders. Later, Canadian Prime Minister Pierre Trudeau referred to it sarcastically during a complaint about the ritual speechmaking that characterized the Bonn summit.

The combination of Reagan's unshakable anti-communism and his lack of sophistication in dealing with complex questions raised questions among some Europeans whether his words of peace would be followed with deeds.

Le Matin in Paris wondered aloud: "Can we be sure that any agreement made by Reagan would be followed up by concrete steps?"

The Times of London, basically supportive of Reagan and his themes, found his speech to Parliament "perplexing" because of the absence of practical policies to carry out his moralizing. The Times concluded that it only added to the "confusion among allies, adversaries and members of his own administration" on foreign policy questions.

In London, the Washington Post's correspondent, Leonard Downie Jr., reported that diplomatic sources concluded that British Prime Minister Margaret Thatcher "completely dominated" Reagan in their talks and made it impossible for him to have any influence on her conduct of the Falklands crisis.

Reagan's well-written speech to members of Parliament, perhaps the most systematic exposition he has ever given of his anti-Soviet views, won praise for its delivery from middle-of-the-road members of both parties but was considered as irrelevant to current world crises by many of these same politicians.

One up-and-coming Conservative member of Parliament, who is known as a student of American politics, described the address as "the kind of speech I would expect a mediocre Conservative member of Parliament to give to his local Rotary Club."

What was striking about the address to those who liked it was the effective way Reagan evoked World War II sentiments, which have been resurgent in Britain since the Argentine seizure of the Falklands.

World War II metaphors are never far from Reagan's mind. In his remarks at Templehof Airport, where he told campaign stories about the death of a World War II pilot under heroic circumstances and the murder of Leon Trotsky, Reagan referred to American airmen and their dependents in World War II terms, saying that the American people "just know you are their G.I. Joes and Jills and they love you, too."

What may have prevailed for Reagan in Europe were the same qualities that carried him through the 1980 campaign. On television and in his ceremonial appearances, Reagan came across as a natural man, and one so genuinely friendly that it was hard to think of him, for all his reverence for martial heroes, as a president who would be willing to launch a nuclear war.

Reagan made his share of gaffes along the way. In his radio address to the American people he referred to Italy as a "worm" country instead of "warm." He was so over-scheduled and became so tired that he nodded briefly during his meeting with the Pope and arrived late at Windsor Castle for a welcome by Queen Elizabeth II. His concluding speech at Bonn struck some of those who heard it as being as simple-minded as it was undoubtedly sincere.

But Reagan broke through on a human level, demonstrating the natural political qualities which carried him to the presidency.

"The president turned out to be a genial man, a walking tribute to the avoidance of jogging, health foods and psychoanalysis," wrote Frank Johnson in The Times of London after Reagan's speech at Westminister. "It was a privilege to have him among us."