President Carter's lightning stopover in this "Capital of Europe" Friday will come at a time of deep-seated change in the Atlantic Alliance and of increasing protectionist pressure in the Common Market.

At NATO, Carter will meet with its secretary general, Joseph Luns. The economic and trade issues, focusing on the consequences in Europe of Japan's large trade surplus and the weakened dollar, will come up in Carter's talks with Roy Jenkins, president of the European Economic Community's executive commission.

In this firs visit to NATO head-quarters, President Carter is expected to repeat American assurances - given here last month by Secretary of State Cyrus Vance - to counter European concern that U.S. detente policy implies a reduced military committent to Europe's defense.

In contrast, Carter will be seeking rather than providing reassurances at Common Market Headquarters, where recent protectionist moves have alarmed American officials. The President will seek evidence that the EEC remains committed to further trade liberalization.

The importance of the issue is reflected in the fact that this will be the first visit of an America President to the headquarters of the nine-nation European Community.

Carter comes in a period of European economic disarray, with flagging performances by the major nations and rising unemployment. Obervers here concur that the economic uncertainty has aggravated tensions between the United States and the Common Market, while at the same time eroding some NATO members'financial commitment to the collective defense of the continent.

"Carter is coming at a time when the political and military situation in NATO is in a state of flux," said a European diplomat, discussing the "all-pervasive" priority now put on arms control by the U.S. administration. Europeans are disturbed by the vulnerability that might result from the conclusion of a new result from the conclusion of a new strategic arms limitation treaty with the Soviets and from progress in the troop reduction talds under way in Vienna.

For most European governments, however, it is "politically unthinkable," says an alliance source, to envisage increased spending on military manpower at levels needed to calm these fears. Britain, the Netherlands, Portugal and Turkey are among those reportedly reluctint to meet even the modest 3 per cent increases targeted by the alliance in the medium term. So, like it or not, say defense experts, "Europeans are having to pay the price of SALT" and the Vienna troop talks - a price paid in the coin of military anxiety rather than hard cash.

Another touchy political issue is the production and deployment of the neutron warhead. European governments are seen here as privately convinced of the weapon's value as a tank stopper but would be happier for political reasons to have the decision appear to be imposed on them by President Carter. The weapon is controversial because it would be designed to kill concentrated enemy troops while limiting ther physical damage.

The neutron issue aside, Europeans are now keenly aware that Carter, deeply committed to pursuing military detente, judges that the time is ripe to strike an arms control bargain with the Soviets. They also look to the President, strongly identified in European minds with the causes of human rights and nuclear nonproliferation, to reestablish the "moral highground" that was America's before the Vietnam debacle, say diplomatic sources.

Carter's taks with Jenkins of the ECC will reflect the concern both have expressed about the protectionist threats against the international economy dominated by the U.S. EEC-Japan triangle.

But Europeans, particularly Chancellor Helmut Schmidt of West Germany, are also alarmed by the spiraling U.S. deficit, seen here as mainly caused by oil imports, and the slumping dollar - which has reduced the competitiveness of EEC exports. Strong EEC backing for the President's energy program reflects the belief that its adoption by Congress would strengthen both the U.S. trade position and the dollar.