PARIS — For Adam Kirkwood, a weekend getaway in Paris that included museum visits and strolls along the Seine had gone pretty smoothly.

Until it was time to go back to London.

On Monday, he experienced a flavor of France’s protest culture combined with a taste of Brexit when his Eurostar train was delayed for two hours at the Gare du Nord. The wait was caused by a French customs officers’ protest against what they see as France’s lack of preparation ahead of Britain’s exit from the European Union.

“I am not sure that we, in Britain, are as worried as the French customs officers about Brexit,” Mr. Kirkwood, 68, said. “Maybe we should stop drinking tea and start thinking about what comes next.”

As Britain prepares for another crucial vote on Tuesday about the withdrawal, customs workers on the other side of the English Channel have been showing what might happen. Without extra funding and staffing ahead of the March 29 deadline, they say, the ports, train stations and tunnel linking Britain and France will face mayhem.