President Carter's decision to shun higher tariffs and seek voluntary limits on low-cost shoe imports has evoked a sight of relief from the European Economic Community, which said the move showed "concern for preserving an open world trading order."

The restraint exercised by Carter has buoyed hopes at Common Market headquarters here that the administration's trade policy will eschew protectionist measures for ailing U.S. industries.

The EEC's Executive Comission "noted with satisfaction" Monday that European shoe exports, mainly expensive ltalian brands, will not be affected by the President's action. The planned quotas will be aimed at cheap footwear imported from Taiwan and South Korea.

Still mired in deep recession, the community is running severe trade deficits with its industrialized partners. Last year the U.S. racked up a $7.3 billion surplus and Japan earned a $4 billion surplus in trade with the nine EEC countries.

Despite pressures from labor unions and industry to erect new trade barriers, most European governments have refrained from doing so in the realization that their economies would suffer the most from global protectionism.

"ln the trade war with the United States, there is really no sector in which we could retaliate," remarked one EEC official. "We would do more damage to ourselves."

lnstead, the Europeans have turned on the Japanese and demanded a sharp cutback in steel cars and electronic gear sold in Europe - or a massive Japanese buying campaign of goods, especially agriculture, produced in Europe.

Japan has pledged to trim its commercial clout in Europe through methods short of protectionism, but so far the results have been far from satisfactory to EEC nations.

Squeezed by a yearly oil import bill of $67 billion and the onslaught of American and Japanese goods, the common Market countries have tried to develop markets elsewhere to pull their industries out of recession, but with little luck.

The community has taken great pains to build trade links with Eastern Europe and the Soviet Union, but the Communist countries insist on buying most goods on credit. Trade with the Third World has grown but developing nations are also plagued with economic woes and have not evolved yet into major markets for European industrial and farm goods.

Faced with dwindling foreign markets, the Common Market has been hoping for a more open trade policy from the United States. But given their current economic vulnerability, the community countries, except Germany, find they have few economic concessions to offer in return.

ln their initial contacts with the Carter Administration, some European leaders emphasized that a more liberal American trade policy could have salubrious political, as well as economic, effects in Western Europe.

Opening the door wider for imports from Europe, they claim, will enhance employment prospects and helpEEC governments stave off the rising challenge of leftist parties.

The question of how to reflate the economics of the United States, Japan and West Germany to improve trade and jobs prospects in weaker Western countries is emerging as the most crucial topic on the London economic summit agenda for May 7-8.

The community is expected to press its trade case against Japan, and to encourage Carter to stand firm against the sirens of protectionism echoing from Labor, industry and congressional circles in the United States.