PARIS, April 8--Under the threat of a Communist takeover in Laos, the United States, Britain and France strove tonight to adjust their differences in Asia and Europe. President Charles de Gaulle's government exhibited a new spirit of cooperation.

The French leader personally received U.S. Secretary of State Dean Rusk at Elysee Palace in the first high level American-French encounter since De Gaulle turned his back last January on a U.S. plan for a multination nuclear force in the North Atlantic Treaty Organization.

American sources said both men expressed concern over the deteriorating situation in Laos, which Rusk had introduced at a ministerial meeting of the Southeast Asia Treaty Organization earlier in the day.

The 70-minute De Gaulle-Rusk meeting was described as relaxed and friendly. Their wide-ranging discussions, informants said, also touched on such questions as Cuba and the NATO nuclear force, now attracting some French interest.

British Foreign Secretary Lord Home and French Foreign Minister Couve de Murville met for the first time since Paris-London relations were strained severely last January by France's veto of the British bid for membership in the European Common Market. The atmosphere of their 25-minute meeting was cool, but the fact of meeting itself was considered significant.

De Gaulle's premier, Georges Pompidou, pleased both the Americans and British by opening the three-day SEATO meeting with a pledge of France's "full cooperation" in SEATO's peace-keeping endeavors.