The leaders of France, Britain and West Germany are becoming increasingly preoccupied with domestic challenges to their governments, a development that political analysts believe may portend a slackening of European influence in international affairs.

Faced with mounting political and economic troubles in a period leading up to elections, French President Francois Mitterrand, British Prime Minister Margaret Thatcher and West German Chancellor Helmut Kohl are expected to devote more attention to their internal difficulties and less to pursuing foreign policy initiatives that generally carry little influence with voters.

The views of the French Socialist president and British and West German conservative leaders have coincided most frequently in East-West and security issues, where their extraordinary harmony contributed to the successful deployment of new nuclear missiles in Western Europe despite intense opposition from the Soviet Union and antinuclear activists.

Last year, when Moscow and Washington virtually froze contacts following the collapse of arms control talks, the Paris-London-Bonn triangle led the European diplomatic campaign to perpetuate dialogue between the two blocs and to encourage the two superpowers to return to the Geneva negotiating table. But now, as Moscow and Washington seem mired in a new impasse over space weapons and unable to decide about a summit, the major European allies are turning inward to deal with their own problems rather than placing overriding emphasis on the revival of detente.

Such parochialism appears likely to block early progress toward changes in the European Community. Even an ardent pro-European such as Kohl has felt compelled in recent weeks to hold up agreement on grain prices because he fears a political backlash from German farmers who want higher subsidies.

The tendency to appease powerful national lobbies seems bound to grow as the three leaders become increasingly worried about their vulnerability in forthcoming elections, beginning with the French parliamentary vote next spring.

Mitterrand's party is expected to lose its majority in the National Assembly to conservative forces, raising the prospect of an unprecedented clash between a Socialist president and a right-wing legislature.

A similar swing against the incumbents has been shown in Britain and West Germany, where the ruling Tory and Christian Democratic parties have suffered resounding defeats recently in local and state elections.

This month, the British Conservatives lost control of nearly half the county governments in England and Wales where they previously held majorities. National opinion surveys indicate that the Tories now trail both the Labor Party and the fledgling alliance of Liberals and Social Democrats.

Thatcher's personal popularity has plunged from the heights she enjoyed from the Falklands War through last March's victory over striking coal miners, and many backbenchers in her own party are discontented with her leadership.

Kohl's governing capabilities also have come under fire from fellow Christian Democrats following their severe setback on May 12 in North Rhine-Westphalia, the country's most populous state, where one-third of all West German voters live. The Social Democrats won an absolute majority with more than 52 percent of the vote, while the Christian Democrats fell to less than 37 percent, their worst showing ever.

Although his party still ranks ahead of the opposition Social Democrats in the polls, Kohl is facing growing pressure from his party to display more aggressive leadership in making unemployment the foremost priority of the center-right ruling coalition in Bonn.

Last week, a member of Kohl's Cabinet, Interior Minister Friedrich Zimmermann, criticized the chancellor for his dithering ways and said, "His leadership must become more visible."

After the welcome demonstration of western unity during the "Euromissile" crisis, the Reagan administration now confronts the possibility of less cooperative behavior among its major European partners as they strive to recover from their weakened positions at home by appealing to electoral rather than to strictly alliance considerations.

Moreover, some commentators in Europe believe that Washington may soon feel more obliged to orient its foreign and security policies in ways that might bolster the sagging political fortunes of sympathetic governments in Europe.

The Reagan administration might be untroubled by Mitterrand's problems, as a Socialist loss might usher in a more like-minded conservative leader in Paris. But the foreign policy repercussions posed by the potential fall of Thatcher and Kohl are far more severe, primarily because a sweep to power by their Labor and Social Democratic opponents could mean dramatic changes in British and West German policies toward arms control and NATO.

If the stalemate in the Geneva arms talks persists, Kohl is likely to come forward next year urging new American disarmament initiatives so that his support for the U.S. negotiating position would be vindicated before national elections are held in March 1987.

"Ironically, weakness at home could spell more influence in Washington," said Karl Kaiser, director of the German Society for Foreign Policy, a leading West German think tank. "Considering the alternative foreign policies if governments in Bonn and London change hands, the U.S. administration will not want to undermine the position of friendly leaders like Thatcher and Kohl."

The leaders in Britain, France and West Germany are expected to focus most of their time and energy to boosting the economy and easing unemployment in the period before elections, but some foreign policy shifts are likely to be influenced by political concerns as well. Unlike the impassioned debate over the missile deployments, the controversy over President Reagan's Strategic Defense Initiative is thought to be too esoteric to affect votes.

"With the Pershings, you were actually putting something seen as dangerous and alarming on our soil," a senior policy-maker in Bonn said. "But SDI is far removed and not even a reality, so it does not have any of the same kind of political impact."

Nonetheless, the nature of Europe's role in the program -- whether it would be too subservient to purely American needs -- and the risk of a "brain drain" of European scientists flocking to the United States have become contentious political issues in many European countries.

France has proposed a European program, called Eureka, to promote space and high-technology research for civilian purposes that would overlap with the SDI program. Britain and West Germany have expressed skepticism about the high cost of a project that would duplicate aspects of SDI, but lately they have warmed to the idea as a way to enhance a European voice in space technology.

"SDI is not going to win or lose votes," a foreign-policy official in London said. "But the political danger is that the public might tend to see our cooperation with SDI on the low-tech end as a kind of humiliation. That would not be welcome."

In Eureka, Mitterrand sees valuable political gains to be scored in securing Europe-wide support for a French initiative, as well as asserting Paris' traditional line of greater independence from the United States.

Political analysts in Paris believe that Mitterrand now is committed to follow a more "Gaullist" foreign policy, stressing France's distinct views and divorced from U.S. policies, much more than was the case during the first half of his presidency.

As France's first left-wing president in 25 years, Mitterrand quickly set a course after his election in May 1981 to reassure the U.S. and his European allies that France's loyalties were bound to the West.

Mitterrand provided important backing for Washington in the trial of strength with Moscow over deployment of cruise and Pershing II missiles in Western Europe in 1983. He condemned the Soviet invasion of Afghanistan and the suppression of the Solidarity trade union in Poland and did not flinch from straining relations with Moscow by expelling dozens of Soviet diplomats from Paris on charges of espionage.

Some French analysts believe that Mitterrand is convinced that the balance of power has now been restored between Moscow and Washington, affording Paris more maneuvering room to resume its customary middle role between the two superpowers.

"From Mitterrand's point of view, the external environment has improved, but his domestic situation has deteriorated," observed Dominique Moisi, associate director of France's Institute for International Relations.

One sign of a return to France's maverick ways came at the seven-nation economic summit in Bonn in early May, when Mitterrand vetoed agreement on setting a date for a new round of global trade talks. He also declared that France would not join the SDI research program.

Mitterrand's isolation at the summit, and the aggravation he caused his partners, was applauded in France, where his stance was perceived as a valiant defense of national interests. Even right-wing opponents who usually seize any opportunity to criticize him endorsed his positions.

"Mitterrand is using foreign policy as a domestic political plus," Moisi said.

In Britain and West Germany, however, the political climate appears to be largely determined by the state of the economy and unemployment. Foreign policy issues rarely have exerted decisive influence over elections; a recent Gallup Poll found that only 9 percent of Britons questioned mentioned defense as the country's most urgent problem, while 80 percent cited unemployment.

Thatcher's decline in popularity and Tory losses in local elections have clearly reflected public disillusionment with her austere economic policies. Inflation has risen above government predictions to nearly 7 percent, while joblessness has continued to grow. Britain's unemployment rate is now close to 14 percent, more than twice the level than when Thatcher took office in 1979.

Even though she is not compelled to call new elections until autumn of 1988, Thatcher is encountering active dissent within the party over the impact of her policies. A recent British Broadcasting Corp. poll of 200 Conservative Party backbenchers showed that 75 percent are worried that the government was not seen to be doing enough about unemployment.

Kohl is also troubled by stubborn joblessness, now at 2.4 million or nearly 10 percent of the work force. Unemployment was cited as the most important issue in the North Rhine-Westphalia election, and it is expected to dominate the 1987 national campaign as well.

West Germany's Social Democrats already have started a march back toward their centrist roots. Under the influence of Johannes Rau, the North Rhine-Westphalia premier who is widely viewed as the party's likely candidate for chancellor in 1987, the Social Democrats are tempering their hostility toward nuclear missiles and defense spending, while emphasizing the fight against unemployment.

Within Kohl's fractious coalition, his longtime nemesis, Franz Josef Strauss, the head of the Christian Democrats' Bavarian sister party, has resumed carping about Kohl's leadership. Even among top Christian Democrats, there is speculation about whether Kohl's liabilities could endanger the party's chances for remaining in power beyond 1987.