Jimmy Carter's image as an American president able to lead the Western alliance and deal effectively with the Soviet Union appears to be in serious and worsening trouble in Western Europe.

Aftern fifteen months in office, the Carter White House, even in the friendliest of allied capitals, is perceived as lacking a coherent foreign policy. In some places, it is viewed as so unskillful in handling allies and the Soviets as to endanger Western stability.

Over the long run, this view of the president may be proved both wrong and unfair. His good intentions are not challenged. His Middle East policy is cautiously appluaded. And the president's values win praise as a reminder of the distinguishing component of morality needed in Western policy.

Yet, perhaps the gravest of the fears being faced in European capitals are expressed by an experienced French official who travels widely in both East and West.

"The situation is very frightening now. The Soviets have little or no respect for the American administration," he said. "They think it is very soft. You have the exact reverse of Cuba [in the 1962 missile crisis] when the Russians went in thinking they had a soft opponent, and came out concluding the administration was tough. Now, they thought at first the Americans would be tough and are concluding the opposite.

"It is the worst kind of situation.The Russians detest [Zbigniew] Brzezinski," the president's chief national security adviser, "but are not afraid of him."

"In Western Europe," adds another French government official, "this administration is being perceived as weaker toward the Soviet Union than Kissinger ever was in his most conciliatory moments. And the weaker it appears, the more the Soviets use the tactic of accusing the Americans of endangering detente . . . and push Carter to the wall."

West German and British foreign ministry officials tend to reject such a harsh view. In both capitals, more weight is given to internal Soviet problems in explaining the lingering sourness in U.S.-Soviet relations that makes Europeans - caught in the middle - so nervous.

"It has been hard enough for us to try to understand what the president's policies were and meant," says one West German, "so you can understand why the Russians, to this day, still don't grasp it.

"They have been preoccupied by Brezhnev's poor health and by problems in Eastern Europe. Nobody really wants to take responsibility for things with Brezhnev sick. There has been a lack of outward-looking Soviet activity, and so they are less able to understand what is going on in America," he adds.

This view, however, seems more reflective of the kind of understanding found in some allied foreign ministries, where there is more appreciation generally for the intractable problems that any U.S. president faces overseas.

But nowhere, except perhaps among some top British leaders who enjoy excellent relations with Carter, does the president seem to personally evoke clearly positive comments in private discussions.

In some cases, there is the suggestion of allies trying to put the best face on things because they want the president to succeed. "It is hard for use to conceive of things if he doesn't succeed," says one West German.

Yet with the public, in press commentary and among many politicians here, the president seems to be taking a public relations beating.

French and West German officials say that a private and common uncertainty about the president's views, leadership skills and his unpredictability have greatly reinforced the relationship between German Chancellor Helmut Schmidt and French President Valery Giscard D'Estaing.

American and French diplomats, in particular, express concern about U.S.-West German relations. The view that there are few if any people in the White House who pay enough attention or know enough about the Germans is widespread.

The fear is that the unprecedented number of problems that have suddenly - yet steadily - arisen in Bonn-Washington relations under the new administration will at some point alienate the Germans, or lead to political changes here and a conservative assumption of power not foreseen by the White House.

"Someday, we simply are going to turn around, and the Germans won't be there when we need them," said one U.S. diplomat.

Actually, in West Germany, such fears at the moment seem exaggerated. The German political scene is stable, and the Bonn government, at least, seems to be taking its quarrels with the U.S. in stride. A number of thoughtful commentators are also calling for Bonn to pay more attention to its relations with America, and to finally realize that the new American president is indeed different.

But the situation here could easily change. For the most part, President Carter is being portrayed harshly and with mistrust and influential newspapers.

The Carter White House has confronted Germany on virtually every key front of real German interest - economic policy, nuclear export policy, the approach to Soviet human rights violations, and now the neutron bomb.

Even staunchly pro-American politicians here such as the very conserva-leader Franz-Josef Strauss are saying that U.S. defense policy under the Carter Administration has already weakened U.S. credibility, and that a decision by the president not to produce the neutron warheads will undermine the U.S. right to leadership of the Western alliance.

Traditionally, there is always a certain amount of anti-American commentary in Western Europe, which is a function both of American wealth and power and Europe's realization that it must depend on the United States for its security against the Soviet bloc forces.

When the United States was involved in Vietnam, Washington was frequently attacked in Europe. Now the White House is being attacked for failure to pressure the Soviets and the Cubans on their interventions in Africa.

So some of the criticism of Carter may be unfair, or even normal. Yet it seems clearly to be becoming an important public opinion and political factor in Europe, and there seems less certainty about American power and protection.

There is also another difference now. European mistrust of the Russians is also growing. Thus, it is with special frustration that Europeans watch a new strategic arms agreement continue to elude the super-powers while the president makes a tough speech of warning to the Russians at Wake Forest University, and then 10 days later, he postpones a decision on the neutron weapons.

This combination, the influential West German newsweekly Die Zeit noted, will only encourage the Soviets to believe their massive propaganda campaign against the neutron weapon was successful, "and will confirm them in their view that the president is a vacillating leader.

And, as The London Times commented Friday in an editorial on the president's neutron weapon turn-about, "The Russians are now aware not only of divided opinions in the West, but of President Carter's own reluctance to produce the weapon. In that case, it will ironically need still more determination in the West to exact a realistic price in terms of arms reductions" from the Soviets.

West European officials report that the individuals they deal with in the U.S. government are generally good, and say there is respect for individual cabinet officers. Nevertheless the view is widespread that there is no overall cohesion and leadership in the administration that pulls things together.

The most consistent thing about the administration's foreign policy and the people into whose hands it has fallen, one veteran diplomat remarked, "is an obsession with doing the exact opposite of what Kissinger did."