By extending sanctions against the planned Soviet gas pipeline, President Reagan has provided a strong impetus for closer political cooperation between West Germany and France.

Chancellor Helmut Schmidt and French President Francois Mitterrand, whose relations were strained as a result of Bonn's fears of French Socialist economics and French anxieties about a West German drift toward the East, are preparing, with Britain and Italy, to proceed with the pipeline project in defiance of U.S. aims.

The Bonn-Paris coalition now being forged has begun to attack the critical factors that had strained their relationship. France, with strong defense credentials based on a growing military budget and its nuclear modernization program, is lining up with West Germany to safeguard trade with the Soviet Bloc. In turn, West Germany, a strong advocate of liberal economic principles, is looking for ways to assist France economically while containing the destabilizing effects of Mitterrand's radical economic experiment.

The U.S. pipeline decision and the European response suggest a widening gap between Washington and Europe in their fundamental approaches to the Soviet Union. While the White House sees the Soviet economy as vulnerable to immediate economic pressures, the West Europeans argue for a longer range view of the East-West conflict.

A Schmidt confidant, affirming that the current conflict with Washington is leading Bonn and Paris to more common ground, said: "It wasn't wise for some people in Washington to push the pipeline decision."

A mounting sense here that the United States simply is not listening seriously to European arguments encourages officials in Bonn and Paris to set tactical plans primarily among themselves.

Schmidt's Germany and Mitterrand's France make a somewhat reluctant couple. When the French president took office a year ago, he indicated that he wanted to explore with Britain and Italy alternatives to the tightly knit French-West German ties that had reflected a close personal friendship between his predecessor, Valery Giscard d'Estaing, and Schmidt.

In what looked also like an early overture to the Reagan administration, Mitterrand spoke out strongly in support of alliance nuclear modernization plans. Last winter, his government needed no nudge to condemn sharply the martial-law crackdown in Poland.

As recently as the Bonn meeting of NATO leaders in June, Mitterrand, whose nation does not belong to the military structure of the North Atlantic Treaty Organization, took the symbolically meaningful step of attending the summit dinner. The next day, French Prime Minister Pierre Mauroy delivered a speech to NATO members calling on Europeans to recognize that the U.S. military presence in Europe contributes to stability on the continent.

Such tough talk on defense was also deeply appreciated by Schmidt in his battle with leftist groups opposed to planned nuclear missile deployments and to Bonn's continued membership in NATO. A basis was clearly there in the French statements for a revised, more pragmatic Bonn-Paris working relationship.

There have been signs of its rebuilding for months. Bonn officials have been reluctant to criticize French domestic trends publicly, beginning with the inclusion of four Communist ministers in Mitterrand's Cabinet.

West German concerns about the Socialists' nationalization plans--involving specifically the French pharmaceutical firm Roussel Uclaf, a subsidiary of the West German firm Hoechst--were quietly negotiated away in February.

West Germany also held its tongue when Paris floated proposals for a Europe-wide, full-employment program, which ran against the grain of Bonn's anti-inflation focus. On high U.S. interest rates, Schmidt could join Mitterrand enthusiastically in voicing concern over the damaging impact they continue to have on European economies.

Mitterrand, meanwhile, provided Schmidt a parry when the French signed their new natural-gas purchase contract with the Soviets not long after the West Germans did last autumn, thereby deflecting U.S. annoyance with Bonn.

In circumstances of worsening unemployment in Europe and tension between the superpowers, the French-West German tie has acquired a certain beleaguered air in contrast to the self-confidence displayed by Schmidt and Giscard.

Mitterrand's original inclination to play down a closeness to Bonn was frustrated by his failure to improve relations with other European countries, notably Britain.

At the same time, Paris-Washington ties have soured, not only over the Soviet pipeline project, but also as a result of other economic policy clashes involving steel quotas and export credits to the Soviet Union and its allies. Negative feelings have been compounded by U.S.-French differences over Lebanon.

Schmidt's own outlook also has changed, allowing the West German leader to approach a partnership with France on a less ambitious scale. The chancellor apparently has given up the visionary scheme he had for Europe and East-West relations when he, Giscard and Polish former Communist Party chief Edward Gierek were imagined to be shaping a European detente as an umbrella against U.S.-Soviet political fallout.

This view has been replaced by one that is more skeptical, pragmatic and grim. West German cooperation with France is seen as necessary above all to keep the European Community from collapsing from its economic strains.

It is also thought here that a French president can argue Europe's interests publicly more acceptably than perhaps a German chancellor. Mitterrand's attacks on Washington, for instance, for extending the sanctions against the pipeline to include European companies with U.S. licenses, were more sharply worded than Schmidt's.

Personalities and politics aside, the accumulation of generations of business interlocks--spurred 20 years ago by the historic reconciliation between Charles de Gaulle and Konrad Adenauer--would seem to drive the French-West German relationship on. West Germany has become France's largest trading partner; France ranks among West Germany's top four partners.

More recently, the contacts have branched into the security field. These French-West German bilateral discussions provide the French with a discreet and convenient channel into NATO military thinking and planning and give the West Germans a better, if still vague, sense of French military planning, particularly in the use of France's short-range nuclear weapons.