LE LUC, France — When the French put a draft Constitution for a newly enlarged European Union to a referendum in 2005, Pascal Verrelle voted passionately against it — hoping it would stop the European Union in its tracks. He rejoiced when the effort failed, yet was dismayed when the bloc kept gathering more members and powers, anyway.

At the time, Mr. Verrelle, a former soldier, was a prison director, but he eventually felt compelled to enter politics and joined the far-right National Front. When he was elected mayor of this small town in Provence eight months ago, the first thing he did was to take down the European Union flag from City Hall.

“In 2005, a majority voted against Europe, and we still find ourselves in Europe, by magic,” he said, “and I find it inadmissible.”

Today the European Union is wobbling under the weight of problems encouraged in part by that unchecked expansion — stagnant economies, the euro crisis, new pressures from Russia and deep strains over migration, especially from newer members in Central and Eastern Europe.