“This is a bad day for the European Union when the party with such an openly racist, xenophobic and anti-Semitic program gets 25 or 24 percent of the vote in France,” Martin Schulz, the current president of the European Parliament and the Socialist contender to run the E.U.'s main policy-making body, the European Commission, told a news conference early Monday morning. “The reasons behind such a vote for a party like this party in France is not that people are hard-core extremists,” he said. “They are disappointed. They have lost trust and hope,” he said.

Hailed by Europe’s boosters as a way to hold back a wave of public disenchantment and narrow the chasm between citizens and officials, voting for the legislature began last Thursday under the slogan “This time it’s different.”

But a series of televised debates between the leaders of rival political blocs and other efforts to engage with voters have had scant success breaking through a wall of public indifference to what many Europeans scorn as a remote and overly costly Tower of Babel. The legislature has 24 official languages and shuttles between Brussels, the headquarters of union’s administrative machinery, and the French city of Strasbourg, 270 miles away.

“The European Parliament is predicated on the idea of a European ‘demos,' ” Charles Grant, director of the Center for European Reform, a London-based research group, said, using a term meaning shared political culture. “But if this demos does not exist, the Parliament has a very hard time connecting with people.”

Politics in Europe remains highly local, making it hard to identify Continentwide trends despite regular pleas from officials in Brussels that voters need to think more as Europeans and widen their horizons beyond national borders. Voter turnout slumped in 17 countries, including Italy, Poland and the Czech Republic, but rose in 11 others like Sweden and Germany.

Aside from its efforts to restrict snooping by American intelligence agencies in the wake of revelations by Edward J. Snowden, Mr. Grant said, the European legislature “exists inside the Brussels bubble and doesn’t talk about things most people care about.” Its principal concern, he added, “has been to get more power for itself and more money for the European Union.”

The entire assembly decamps once a month to Strasbourg, only to return to Brussels a few days later at a significant cost to taxpayers. Scrapping the trips to Strasbourg would save about $140 million a year.