The great expectations of the White House inner circle for the potentially favorable impact of President Reagan's European trip are being matched increasingly by a sense of foreboding.

Until the Falklands crisis erupted, the trip seemed perfectly timed for a president whose popular support has been eroded by a continuing economic recession and the failure of Reaganomics to deliver on many of its promises. White House polls, however, show that approval for Reagan on foreign policy issues has remained surprisingly high.

Furthermore, the president still is viewed by a majority of the public as having strong leadership qualities, even though an increasing number of Americans don't like the direction in which Reagan appears to be heading. In this context, the European trip seemed an opportunity to reinforce his image as a national leader who stands for the best interests of America.

Now, Reagan advisers are concerned that the Falklands war will expose as symbolism without substance the economic and NATO summits to be attended by the president. They have similar concerns about such dramatic televised spectacles as his meeting with Pope John Paul II. The reality of the war was driven home in a trip-planning session last week by Secretary of State Alexander M. Haig Jr., who said the continued warfare casts "a grave cloud" over Reagan's prospective visit to London.

Others on the White House staff, including national security adviser William P. Clark, expressed similar concerns. But the issue was not put to Reagan for a decision because of uncertainty about what the Falklands situation will be by June 7, when the president is scheduled to visit London after a short stopover in Rome.

If the Falklands battle is raging on that date, Reagan may decide not to go to London or at least to reduce his schedule in Britain. He now plans to address Parliament, dine with Queen Elizabeth II and confer with Prime Minister Margaret Thatcher.

"Even though we've made certain commitments, the president's presence in London could be pretty upsetting to our Latin friends," one White House adviser said shortly after learning of the British invasion of the Falklands.

There is another, more personal, concern about Reagan's trip. Put simply, it is the worry that the president, whose schedule usually is loose, has been relentlessly overscheduled in Europe by a series of additions to his itinerary. These are referred to in the White House as "racheting."

"Racheting" means that every time some country or official made a claim for a meeting with Reagan, a counterpart did the same. These claims were so heavy that even White House deputy chief of staff Michael K. Deaver, who usually succeeds in scheduling rest time for the 71-year-old Reagan, was unable to fend off a schedule that will put Reagan on the go morning, noon and night for nine days after an initial day in Paris to recover from jet lag.

"The president could come out of this trip in great shape," an aide said last week. "He could also wind up a basket case."

The White House has no choice except to make the best of it. Those who say Reagan is up to the mark point to his performance in the New Hampshire primary of 1980, where he showed a determined day and night burst of energy for two weeks after a lackadaisical losing performance in Iowa.

More about the summit: the White House still thinks that Reagan will meet Soviet President Leonid I. Brezhnev at an October summit in Europe. Despite official denials that the White House is actually planning the summit, one adviser notes that nearly every neutral European country has applied to host the summit. The list, in no special order, includes Austria, Finland, Switzerland and Ireland.

More about those Reagan polls: The good news, from a White House point of view, is that the president has to a large degree defused the nuclear-freeze issue. Surveys show that the president's arms reduction proposal is regarded favorably by much of his middle-class base. The bad news is that the "fairness" issue remains indelible, even among some voters who otherwise support Reagan. More voters are giving the opinion that Reagan is a rich man's president.

And more about the White House staff: Attorney General William French Smith will stay on the job, maybe longer than anyone thought, because his acceptance of a $50,000 severance fee from a steel company owned by Reagan pal Earle M. Jorgensen now makes Smith an unlikely candidate for the next Supreme Court vacancy.

However, few in the administration are bullish about the job security prospects of Secretary of Labor Raymond J. Donovan. The prevailing view among White House advisers is that Donovan is unlikely to survive the investigations into allegations about his purported dealings with organized crime figures.