Paris — Despite strongly criticizing Moscow for the military crackdown in Poland, France has just signed a multi-billion dollar natural gas contract with the Soviet Union.
It is the biggest commercial East-West deal signed since the Dec. 13 declaration of martial law in Poland.
In deciding to go ahead, France has asserted its independence, defied the United States, and chosen a different course from some of its West European neighbors.
The timing of the deal, a little less than six weeks after the Polish coup, is especially controversial. The Italians have suspended their gas negotiations with the Russians, and Belgium is making noises that it will not go ahead with a gas deal of its own.
The French natural gas contract with the Russians was signed Jan. 24 over strenuous American objections.
The French government had approved the general form of the contract in early December. There was speculation, though, that after the events in Poland the French might reduce the amount of gas contracted.
But the agreement Gaz de France announced here Saturday calls for eight billion cubic meters of gas to be delivered annually, starting in 1984. That is ''the amount we always wanted,'' said Pierre Guerin, spokesman for Gaz de France.
Since France already buys four billion cubic meters of gas annually from the Soviet Union, the new agreement means that by 1990 the Russians will be supplying 35 percent of French gas needs. The West Germans signed a similar contract with the Soviet Union last Nov. 20.
Washington fears that this level of Russian gas sales to Western Europe will give the Russians too much leverage over the allies. There is also American dissatisfaction with providing the Russians with a substitute foreign currency earner when its oil sales to the West are decreasing, according to an American diplomat here.
President Reagan expressed these concerns to French President Mitterrand at the summit last July in Ottawa. He sent Under Secretary of State for Economic Affairs Myer Rashish here in November in a last ditch effort to force cancellation of the contract.
But the French ''consistently viewed the project as a risk that could be taken,'' the American diplomat said. Faced with decreasing domestic supplies and imports from Holland, the French have been forced to look around the entire world to satisfy their gas needs.
Gaz de France spokesman Guerin said the company had reopened negotiations Friday with Algeria for gas, and was continuing its efforts to secure supplies from Nigeria, Cameroon, and Canada.
As a result, Mitterrand's chief economic counselor, Jacques Attali, has argued that France will not be excessively dependent on Soviet gas. In a crisis, he says, France will be able to absorb a Soviet cutoff by importing from other sources.
In addition, spokesman Guerin said, ''If we didn't take the gas it was evident that other European countries would have taken it.'' He also noted that compared with Algeria, for example, ''the Soviets have been one of our most reliable suppliers.''
The French deal moved the influential daily Le Monde to editorialize that ''the Soviet-French contract was signed at a bad moment,'' and makes French condemnation of the events in Poland ''a whiff of oxygen.''
A French Foreign Ministry spokesman refused to elaborate on the timing of the accord. He emphasized that it was a contract signed by Gaz de France, a national enterprise, and Soyouzgas Export, subject to French government review.
But Gaz de France sources said such approval was ''a mere formality,'' since Mr. Attali, Minister of Foreign Trade Michel Jobert, and even Foreign Minister Claude Cheysson were intimately involved in last week's final negotiations.
American diplomatic sources speculated that the French signed now, well aware of the embarrassment it would cause, because the Russians gave them a good price.
Although Gaz de France refused to release the agreed price, the Americans said they probably received at least as good a deal as the West Germans, $4.65 per million BTUs (British Thermal Units).
''The French had decided it was a project they needed, regardless, so it was never put into jeopardy,'' the American diplomat said, noting, ''they may have had qualms about the timing.''