ON TAKING OFFICE, the new foreign minister of France, Claude Cheysson, went out of his way to reassure Americans that his incoming government will be a "reliable partner." That's a pleasant gesture. But, as seen from this side of the ocean, the last French government was not such a model of warm and predictable cooperation that Mr. Cheysson needs to fear irremediable shock and distress here at its departure. That's good reason for both Americans and Europeans to be concerned about erosion of the alliance and its sense of common purpose. But those concerns arise from a wider pattern, of which the French elections were only the most recent example.

On both sides of the Atlantic, in the past several years, voters have been demonstrating a rising sense of exasperation with politics-as-usual. Governments leaning to the left have been abruptly replaced by the right; governments leaning to the right have been replaced by the left. In that sense the forces that brought Mrs. Thatcher to the top in Britain, and Mr. Reagan to the top in this country, have something in common with those that have now made Mr. Mitterand, a Socialist, the president of France. Inflation is deeply unpopular -- but the methods of reducing inflation are equally unpopular, and people have tended to vote angrily against both.

There has been no severe worldwide collapse of living standards, as there was in the 1930s. But people had expected their incomes to keep rising rapidly, as their political leaders promised. Unemployment is up well beyond the accustomed rates in most of these countries. Public benefits designed in the expectation of strong and continuous economic growth are under varying degrees of strain, and that frightens the beneficiaries. The troubles of Social Security in the United States have their European parallels.

The politics of poor economic growth usually comes to international attention only when it affects international concerns -- like military security. After the Dutch elections today, for example, the rest of NATO will read the returns anxiously for indications of strength of the pacifist movement and clues to the Netherlands' decision on the deployment of the medium-range nuclear missiles. But Dutch opinion on weapons is not unrelated to Dutch distress about the way things are going at home. Dutch wages have far overshot the economy's ability to pay them, and unemployment is consequently soaring, which in turn is swelling welfare programs and throwing public budgets wildly out of balance. The North Sea gas wells that have, so far, paid the bills will sooner or later be exhausted. Those are the concerns that set the climate in which a country makes decisions about security, and not the other way around.

The recent elections in the major Western countries, both here and in Europe, have brought to power people who, although not radicals, are well outside their countries' established centrist traditions. Most of them have come to office with firm ideological commitments. Most of them are deeply preoccupied with the condition of their domestic economies, to which they give absolute priority over international affairs. Reliable though the major partners of the alliance will remain, its affairs are evidently going to be conducted in an unusually contentious and abrasive style. Over the next few years, inflation rates may be a better indicator of the state of the alliance than the arms budgets are.