“The E.U. may strengthen if it demonstrates measures relevant to the crisis and if it can use its scale to overcome the limitations of purely national policies,” he said. But the fuss over borders is exaggerated, he added.

“The virus travels with the person, so borders are relevant,” he said. “People talked about how catastrophic it was to have temporary borders between France and Germany, about Europe splintering,” Mr. Heisbourg added. “But not everything is geopolitical. You can’t fight this without borders. It’s about the logic of taming the epidemic.”

If populists criticize the performance of Brussels, the pandemic is also an argument for giving Brussels more power over health research, standards and the coordination of policies, he argued.

Mr. Zuleeg agrees. “When it comes to cross-border issues like this we need to set up ways to react quickly,” he said. “We had to do it in the financial and monetary field with the debt crisis, and now we’ll have to do it in health. Not because someone wants ‘a bigger Europe,’ but because we need to do it. We are interdependent across borders.”

Monika Pronczuk contributed research from Brussels.