Domestic political considerations have encouraged France and West Germany to step up the search for a way to break the deadlock between Moscow and Washington over a new generation of missiles in Europe.

As the December deadline approaches for beginning the deployment of U.S. medium-range missiles to counter the Soviet buildup of SS20s aimed at Western Europe, leaders in Paris and Bonn have shown an increasing interest in avoiding a showdown. They have, in effect, abandoned an earlier policy of saying nothing that might prejudice the outcome of U.S.-Soviet negotiations in Geneva and have publicly, albeit tentatively, endorsed a compromise proposal rejected by both superpowers.

Under the compromise, which was hammered out in private by U.S. and Soviet arms negotiators during a secret stroll in wooded hills near Geneva in July last year, each side would be limited to 75 "Euromissiles" apiece. The United States would install only cruise missiles in Western Europe, forgoing plans to deploy the much faster Pershing II, and the Soviet Union would dismantle most of its existing SS20s.

The "walk in the woods" formula appeared to die an early death when it was formally disowned in Washington and Moscow. A year later, however, it is again attracting intense political interest in Western Europe and seems to have provided Chancellor Helmut Kohl and President Francois Mitterrand with their principal subject of discussion at this week's informal Franco-German summit.

Shortly before the meeting, which was held in the eastern French village of Dabo, the compromise formula was endorsed publicly by West German Foreign Minister Hans-Dietrich Genscher. In a radio interview, he said it took into account both the "Soviet Union's security needs and also the West's legitimate interest that the talks concern only American and Soviet missile systems."

After Genscher's remarks, the official government spokesman, Peter Boenisch, issued a statement saying, "There is no discussion at present of renouncing elements of the dual-track decision such as the mix of weapons to be deployed."

A month earlier, in a television interview, Mitterrand said the "walk in the woods" package offered "a reasonable enough basis" for a settlement in Geneva. This, too, marked a slight shift by Mitterrand away from his previous position of unconditional support for U.S. negotiating efforts at the intermediate-range nuclear force negotiations in Geneva.

Both Mitterrand and Kohl remain strongly committed to supporting the deployment of American missiles in Europe if those negotiations fail. For very different reasons, however, both leaders seem to have a common political interest in promoting a compromise at Geneva.

The Bonn government faces a revival of demonstrations against the planned deployment of 108 Pershing II and 96 cruise missiles in West Germany beginning at the end of this year. The opposition Social Democratic Party and the trade unions have decided that they may participate in some of the protests against the missiles and there is always a possibility of violence erupting in the streets.

Mitterrand's motivations are rather more complex. The peace movement is negligible in France, which boasts its own independent nuclear deterrent. No U.S. missiles are scheduled to be deployed on French territory, so there is no need to worry about demonstrations. The problem is economic rather than political.

Predictions of a "hot autumn" in France following the summer vacations are based on the fact that, for the first time in many years, the purchasing power of ordinary French citizens is falling as the government attempts to impose a package of long-delayed austerity measures that will lead to higher unemployment and lower economic growth.

To reduce social tensions to a minimum, Mitterrand needs economic help from Bonn. He also needs the continued good will of the Communist Party, the junior partner in his Socialist-led coalition, which holds the key to industrial peace through its control over the country's largest trade union.

Relations between the two parties recently have become strained because of the Euromissiles issue. In a communique in Moscow last week, Communist Party leader Georges Marchais echoed Soviet calls for the inclusion of France's nuclear forces in the intermediate-range missile negotiations. This is totally at odds with the official French position.

On the face of it, the "walk in the woods" formula lets both the French and the West Germans off the hook. In Mitterrand's eyes, it has the virtue of omitting French and British forces in the calculation of a new nuclear balance in Europe. And, because it envisages significantly lower American deployment, it would also give the Bonn government a respite from antinuclear protests.