The most unpopular American in Europe right now, at least among a small and bedraggled band of his countrymen is Zbigniew Brzezinski.

Brzezinski, the White House national security adviser, was the chief architect of President Carter's holiday journey overseas. It was Brzezinski, and Carter himself, who thought it would be good to start the new year with a mind-numbing journey to seven nations in nine days, hopscotching 18,000 miles halfway around the globe and back.

Originally, of course, Brzezinski thought it would be even better to travel 25,000 miles, to nine countries in 12 days. But when that itinerary had to be canceled in November, he settled for something slightly less ambitious.

Brzezinski and the global thinkers of the NSC concern themselves with the realities of international politics. They do not think about, or have much experience with, the logistics of moving several hundred people at breakneck speed around the world. In planning this trip, they seem to have thought of everything but one important human element - the fatigue factor.

The fatigue factor produced some funny moments: Stanley Cloud of Time magazine sitting down in his hotel room in Paris to have a cigarette and waking up several hours later, at 3 in the morning. It also had its not-so-funny moments. John Osborne of New Republic magazine, who is in his 70s, was hospitalized in Paris. He expects to return to the United States early next week.

What is important is not that the press is complaining about Brzezinski's talents as a scheduler - we are always complaining about something - but that the lessons of this journey have not been lost on Carter's White House staff.

Carter is loath to admit any human weakness, but even presidents are not impervious to fatigue. He had some misteps - a careless remark in New Delhi that was recorded and marred the warmth of that particular visit - and some missed opportunities when he seemed just too tired to do better.

"With this kind of schedule, he [Brzezinski] gets what he paid for," one member of the White House party said in Paris. "He gets the President tired, talking into a live mike at a photo session. He gets lots of things."

One of the President's worst moments came near the end of the trip and should have been one of the trip and should have been one of his best moments. The setting was an American cemetery on a bluff above Omaha Beach on the Normandy coast. It was a moving scene that touched everyone, but Carter's disjointed remarks hardly lived up to the moment and seemed all the worse when contrasted with the eloquence of French President Valery Giscard d'Estaing.

Afterward, White House press secretary Jody Powell was furious with speechwriter James Fallows for not supplying the President with a brief text. But who knows whether Fallows - a talented writer who produced Carter's widely praised speech in New Delhi - could have by then written much better than the President spoke.

"You know," one presidential aide confided as the buses pulled away from the Normandy beaches, "This was an NSC operation from beginning to end. And I didn't think you are going to see anything like it again."

Powell was angry about the Normandy performance because it was such a missed opportunity, the ultimate media event on this trip to be beamed back to Carter's constituents in the United States. Whatever was accomplished in the President's private meeting with several world leaders, it was television that dominated the trip as it dominates so much around the presidency.

It was planned that way and at every stop Barry Jagoda and Anne Edwards of the White House television office did their best to accomodate the television networks.

White House officials insisted before and during the trip that important business was to be conducted at each of the stops. That may be true, but you could not prove it by most of the American correspondents who accompanied the president. The most substantive information was provided to "pool reporters" aboard Air Force One by Brzezinski and Secretary of State Cyrus R. Vance, both of whom insisted on being identified only as "a senior administration official."

Powell was seldom available and had little to say about substance while it was supposedly going on. His briefing in Paris on the Carter-Giscard meeting, coming on the eighth day of the journey, was the first general meeting he had for reporters. And at that, he didn't have much to say.

It is possible, bounding from one country to another with an American president, to tell something about the shifting currents of wealth in the world.

There was a time when the White House press corps could look forward to receiving some lavish gifts from foreign governments while overseas with a president. There are, for example, fond memories among veteran reporters of expensive perfumes and liqueurs from the French government. In Paris this time, the only thing the Americans found in their hotel rooms was a half bottle of red wine, a gift of the hotel.

But the oil-rich Middle East was different. The Shah of Iran not only threw a lavish New Year's Eve banquet for the press corps, he arranged in advance to pay the hotel charges of the visiting U.S. contingent. Several reporters protested and arranged with U.S. Information Service Officials in Tehran to be billed later. The Saudis tried the same thing, and the clerks at the hotel in Riyadh were incredulous when most American reporters, credit cards in hand insisted on paying.

We take care of our own: At the Shah's New Year's ave party, a television camera crew showed up to shoot some film for a feature story. The film included a scene of a reporter having a grand time dancing with one of the stewardesses from the press planes. But the scene was spotted by a friend of the reporter's, a television correspondent, excised and never transmitted home.

The New Year in Tehran was marked by a couple of half-hearted shouts of "Happy New Year" in the press room. By then, Carter had announced that he would meet with Egyptian President Anwar Sadat and most everybody was too busy to make much of the coming of 1978. When the clock reached midnight in Washington, it was marked by an off-key chorus of "Auld Lang Syne," in bright sunlight aboard the press plane, 37,000 feet over Iran.

It is said that Poland has a national drinking problem and it is no wonder. Vodka sells for $1 a bottle in Warsaw. One reporter purchased nine bottles, all of them, he claimed to skeptical colleagues, for friends back in the United States.

Poland asks provided the finest hotel facilities for the traveling americans. Warsaw's Intercontinental Hotel is plush even by capitalist standards.

The weather in Warsaw was awful, but the gen. consenus was that smog-infested Tehran was the city the U.S. contingent was most happy to leave. India provided the best weather and the best shopping. When the press planes left New Delhi, they contained thousands of dollars worth of Indian rugs and other items.