London — Europe badly needs proof of its capacity to unite and grow stronger. Instead, it is having to face the fact that the people of Europe appear to be losing the faith that inspired them over a quarter of a century ago to thrust narrow nationalism aside in pursuit of broader goals.
As the leaders of the European Community (EC) gathered at Fontainebleau, near Paris, to tackle their economic differences, the malaise that has become a crisis at the heart of Europe appeared more broadly based than budgets, farm policies, and the seemingly perennial problem of Britain's special demands.
Results of elections for the European Parliament showed that voting turnouts for the entire EC were on average 2 percent lower than at the last elections in 1979, despite massive attempts by the political parties to boost public interest in the polling.
And Euro-Barometer, a recent European survey, found a decline in popular confidence in the Community compared to earlier surveys. It also showed Europeans sharply divided over EC issues, and especially hostile toward Britain.
At the London economic summit of the seven leading industrialized democracies , the European voice was notably hesitant. Although Britain, West Germany, France, and Italy all agreed that high United States interest rates were impeding their own growth, they were not prepared to say so openly for fear of offending President Reagan.
Such lack of confidence, leading European officials say, encourages those in the Reagan administration who do not take Europe seriously to look elsewhere for friends.
Significantly, the defense appropriations amendment proposed by US Sen. Sam Nunn (D) of Georgia, which would have partially withdrawn US troops if Europe failed to spend agreed amounts on defense, did not prompt a united response from the other side of the Atlantic.
Instead, the Europeans merely hoped that the amendment would fail.
Europe's problem, it is widely agreed in European capitals, is a lack of momentum. The EC's membership has risen from six nations to 10, but expansion has not found its counterpart in greater unity or in rising economic confidence.
In Britain, where only 32 percent of voters bothered to go to the polls, the belief has grown that the EC is increasingly irrelevant to their attempts to break out of recession.
In West Germany and France, voting was around 57 percent and appeared to reflect apathy arising from high levels of unemployment. West Germans went to the polls while their country was in the grip of a strike of metalworkers which, if it turns out to be lengthy, will severely damage Germany's trading strength.
As they addressed their problems, Europe's leaders thought in terms of ''a new agenda'' to relaunch enthusiasm for united action. Key ideas include:
* A rapid solution to the EC's budget problem, notably Britain's persistent demand for special treatment. Prime Minister Margaret Thatcher was reported to be in a flexible frame of mind. President Francois Mitterrand, who is passing the EC mantle of leadership over to Ireland, was reportedly trying out a new budget solution.
* Promoting unity by greater attention to the defense of Europe. Western European Union, a near-moribund grouping of Europe's leading nations, has met to explore ways of closer defense cooperation. The European members of NATO also see the advent of Lord Carrington as secretary-general as an opportunity to rally round a confident and influential personality.
* A renewed attempt to inspire the creation of a united European voice in relations with the United States. British leaders would like to be able to harness their own good relations with the Reagan administration to the greater good of the EC but say they feel impeded while bickering about the Community budget and other internal matters continues.
On the eve of the Fontainebleau summit, senior European officials were hoping that there would be a breakthrough on the budget, enabling the leaders to concentrate on the larger problem of unity within a market of 270 million people who show clear signs of boredom and disappointment with the current lack of achievement.