When West Europeans in nine countries go to the polls for the first direct elections to the legislative assembly of the European Common Market on June 7 and 10, it will constitute the birth of one of the world's largest democratic voting units, with a combined population of 259 million.

Except for France and Britain, the two countries where the very idea of advancing toward more European unity has become an internal political issue, these first European-wide elections have stirred little interest. In West Germany, a recent poll shows only about 30 percent of the electorate said it would definitely vote, with 45 percent saying it would probably do so. Italy is too concerned with its own parliamentary elections to be held the week before to have focussed on the European Parliament campaign.

Instead of reducing divisions, the European elections seems to be underlining them. In Belgium, for instance, the country was cut into three districts along the lines of the bitter language divisions that have so often degenerated into communal rioting. Flemish-speakers are to elect 13 assembly members and French-speakers 11. Inhabitants of the Brussels capital district, headquarters for most of the Common Market's bureaucratic machinery, must decide individually if they want to vote for Flemish or French speakers.

French President Valery Giscard d'Estaing was probably speaking for most West Europeans this week when he described the old dream of an American-style United States of Europe as being an extreme position these days.

The European Parliament is the legislative body of the European Economic Community. As a body whose 198 members were appointed by national parliaments to represent them, it has so far been largely a debating society. It generally refrained from exercising its theoretically considerable power over the European Community's budgets and to censure and question the community'ss executive commission in Brussels. Now that it is to be made up of 410 representatives directly elected by the voters, the general expectation is that will begin making its weight felt.

This prospect is especially appealing in West Germany, where the European Parliament is viewed as the ideal kind of international forum for West Germans to exercise strong influence. They prefer to work quietly through international organizations in their international organizations in their continuing drive to regain complete reacceptance by their fellow Europeans, many of whom still express anti-German attitudes stemming from World War II.

Each of the European Community's four most populous nations-Britain, France, Italy and West Germany-will elect 81 members, with smaller delegations from the other five countries.

The general assumption that the direct elections will boost the European Community's authority could be disproved if Western Europe's four main political streams-Christian Democrats, Liberals, Socialists and Communists-fall into public squabbling. Already, conservatives all over Western Europe are expressing concern over the likelihood that the combined Socialist parties of the nine member-states will dominate the parliament in Strasbourg, France.

A number of parties are making it clear that they are not even happy about forming transnational groups with their opposite numbers in neighboring countries.

The Italian Communists say they feel closer to the West German Socialists than to the more doctrinaire French Communists. The British Laborities are unhappy about being in the same parliamentary group as the more "federalist" continental Socialists.

Italian Christian Democrats fear their moderate image could be damaged by having to sit on the same benches as Bavaria's Christian Social Union of Franz Josef Strauss, the more conservative sister party of West Germany's Christian Democrats. The European-minded British Conservatives may have trouble sitting in the same group as the ultranationalist French Gaullists.

The community-wide strains within the continent's traditional political groups could eventually lead to some interesting and unexpected realignments back inside the member countries, many analysts think.

For better or for worse, Britain, Denmark, Ireland and the Netherlands will vote June 7. The ballot boxes are to remain sealed for counting simultaneously with those of Belgium, France, Italy, Luxembourg and West Germany after the close of their polling places on June 10. CAPTION: Map, numbers show seats of each country in new European Parliament. By Dave Cook-The Washington Post