By Matthias Verbergt

MAASTRICHT, Netherlands—The picturesque town that gave its name to the pact that created the modern-day European Union is now a bastion of euroskeptics who want to follow Britain out of the bloc.

Town resident Armand Vliegen supported the drive toward a more integrated Europe when the Maastricht Treaty came into force in the early 1990s. But when dozens of asylum seekers recently settled into a converted student dorm about 20 yards from his home, he said his little remaining pro-EU sentiment evaporated.

“The EU is a disaster,” said Mr. Vliegen, a 40-year-old website programmer. “We should have left it already.”

He and many others in Maastricht back the Party for Freedom, whose leader, Geert Wilders, has vowed to steer the Netherlands—a founding EU member—out of the union if he prevails in elections in March.

Recent polls suggest the Party for Freedom could more than triple its presence in the national parliament, capturing nearly 25% of the seats and becoming the leading party in an otherwise fractured political landscape. It and another anti-EU party won the most votes in Maastricht in last year’s regional elections.

Mr. Vliegen’s change of heart reflects the same discontent with the status quo that led British voters in June to opt to leave the 28-nation EU, and that is gaining ground in other member states.

In France, anti-EU politicians have won a string of electoral victories in recent local elections after campaigning against the euro, blaming economic hardship and high unemployment on the single currency. In Austria, polls show anti-EU candidate Norbert Hofer has the edge in October’s redo presidential election, after riding a wave of voter anger over immigration and European integration.

The EU’s struggles with crises such as Greece’s debt burden and the arrival of hundreds of thousands of migrants have fueled disenchantment with Europe in the Netherlands.

An online survey by pollster Maurice de Hond held after the Brexit vote found that only a slight majority of 52% of at least 3,000 respondents opposed a Dutch departure out of the EU and 40% wanted to leave. Another 7% were undecided.

“The Dutch have the feeling they are enclosed in a continental project that isn’t theirs anymore,” said Mathieu Segers, a European history professor at Maastricht University.

That is a sea change. When representatives of the Netherlands and 11 other countries that made up the European Community gathered in Maastricht to sign the treaty in 1992, the goal was to create a binding political structure that would go beyond trade pacts.

The treaty, ratified in 1993, introduced the notion of European citizens and laid the groundwork for a common currency. The Netherlands showed its enthusiasm by agreeing to freedom-of-movement rules for EU citizens and adopting the euro.

In 2005, though, Dutch voters displayed the first strong sign of opposition to deeper integration when nearly 62% of participants in a national referendum rejected a draft EU constitution.

Anti-EU sentiment appeared again during negotiations over Greece’s debt, and the subsequent bailout angered many Dutch voters. “Our money is being thrown out of the windows,” said Mr. Vliegen.

Opposition to the EU is particularly strong in Limburg, the province around Maastricht and Mr. Wilders’s home turf. After the Brexit vote, the Limburg governor, Theo Bovens, proposed that EU and U.K. delegates come to Maastricht to negotiate the separation.

Once a prosperous region, Limburg now lags behind wealthier areas because of the closing of coal mines in the 1960s and 1970s. In last year’s regional elections, the Party for Freedom scored its strongest results in the province.

When Europe last year faced the biggest movement of displaced people since World War II, the Netherlands received nearly 59,000 asylum requests, up from about 17,000 in 2013.

The influx of refugees from the Middle East and Africa prompted Mr. Wilders to call for reintroducing border controls and sparked protests in Maastricht and elsewhere around the country against resettling migrants.

Mr. Wilders scored another victory in a referendum this spring when Dutch voters followed his recommendation to reject an EU trade deal with Ukraine.

After the Brexit vote, which shook financial markets, Dutch Prime Minister Mark Rutte warned against possible copycats. “Everyone who’s inclined to leave the EU, look at the chaos, the complete collapse that we currently see in the U.K.,” he said.

This hasn’t deterred Mr. Wilders. “We want to have nothing to do with the EU anymore,” Mr. Wilders said in an interview. “We want to be a sovereign country, not be at the mercy of nonelected bureaucrats in Brussels.”

Asked about holding divorce talks between the EU and the U.K. in Maastricht, he said: “I would be delighted if the end of the EU formally started in my province.”