DOMESTIC POLITICS ON both sides of the Atlantic have become deeply entwined in the crisis in the Atlantic Alliance over President Reagan's sanctions against Europeans who insist on going ahead with the Siberian gas pipeline. Politics could doom the fence-mending compromise that some Alliance members are now seeking.

Paradoxically, the European leader who was once President Reagan's staunchest ally on East-West issues -- President Francois Mitterrand of France -- has been pushed by Reagan into firm positions that seem to make compromise impossible unless the United States makes a major step forward first.

Senior officials from Mitterrand's Socialist government have made it abundantly clear in recent days that they are not prepared to budge. The Reagan administration created the problem, the French argue, so the Reagan administration should find a way out of it. Mitterrand would clearly prefer no compromise at all to a compromise that could be used against his government by its domestic rivals.

The angry reaction to Reagan's sanctions has created a new political situation in France. The dispute is stoking the already growing fires of protectionism within the Socialist party, and it has led to a resurgence of anti-American Gaullist rhetoric, which Mitterrand had worked hard to diminish during his first year in power. The Communist Party, nominally allied with the Socialists in power, is citing the decision as proof of the dangers of American commercial imperialism. And the center- right opposition offers no sympathy to the Reagan position, because it was Mitterrand's center-right predecessor, Giscard d'Estaing, who signed the French portion of the pipeline deal with the Russians in the first place.

Reagan's sanctions are "the only thing that has brought the big four political parties of France into consensus since Mitterrand came to power," said one French official. Reagan's policy may unwittingly also provide the faltering Socialist government its biggest boost in the important local municipal elections scheduled for March, where Mitterrand can now appear holding high the banner of nationalist resistance to Yankee heavy-handedness.

The message that France is prepared to sit out the winter, waiting for a U.S. reversal, was brought to Washington last week in a very polite but clear form by Jean-Pierre Chevenement, Mitterrand's Minister for Industry, Reasearch and Development and the fastest rising star on the French domestic scene:

"This can, and must be resolved, for French and American relations are much broader and more important than what you are calling the pipeline controversy. For us, there is no controversy over the pipeline. For us, it is a matter of fundamental principles, of the questions of sovereignty, of extraterritoriality, of free trade. We are very attached to these principles, and to nonretroactivity. And the British and our other partners share these feelings."

That sentiment was echoed by Michel Rocard, Mitterrand's Planning Minister and the leading spokesman in the Socialist cabinet for cooperation with private enterprise. "We are sitting quietly, waiting," Rocard said Thursday in Washington. And the same theme was hit hard by Foreign Minister Claude Cheysson in an article written for The Los Angeles Times opinion page.

Chevenement, who met with senior administration officials in Washington last week, predicted in an interview that grave consequences will follow if the dispute is not resolved. "If the sanctions are not removed, you will find European industries very reluctant in the future when it comes to the purchase of American technology and licenses," he asserted, acknowledging that France had decided this summer to begin developing its own national turbine industry "in the context of the sanctions, which certainly had some effect on this matter."

It was the supply of American-designed but French-manufactured turbines to the Soviet Union that triggered the imposition of sanctions. The French decision to go after an independent turbine industry has already contributed to the cancellation by the state-owned RATP (Paris Regional Transport Authority) of a $4.3-million contract with Allison, a General Motors subsidiary, for the purchase of turbines. The contract has been awarded instead to Hispano-Suiza, a nationalized French firm that that will charge about 6 percent more for the job.

Not surprisingly, the pipeline dispute has revived the ideas of national grandeur and independence patented by Charles de Gaulle. Chevenement -- who himself has always been something of a left-wing Gaullist -- noted the parallels between this dispute and the bitter battles of the 1960s:

"This is the first time since the question of NATO was raised by de Gaulle that the question of sovereignty and territoriality has become an issue between France and the United States," he said. "We thought it had been settled, and that raising it again could only cause damage to a relationship that we value.

"One of reasons that France developed its own nuclear technology was that the United States refused to provide France with some military computers. It was said that American law prevented the transfer of certain scientific knowledge on atomic matters. So we did it ourselves, with a lot of investment and work on our part. We never wanted on principle to go it alone, particularly since the United States is so strong in technological development. If cooperation is possible, we prefer it. If it is not, well . . . we would hope the United States would understand that it needs solid, strong allies, and particularly a solid, strong France in Europe as it is today. No alliance could survive as a collection of client countries. None."