It took Europe a half-century to integrate its economies. It took the new coronavirus only weeks to roll that back as countries closed their borders.

Across vast fields of the northern Netherlands, the huge springtime flower harvest is wilting because demand has plummeted, export markets closed and seasonal workers can’t cross the border. Luxembourg has struggled to staff hospitals because nearly half its workforce commutes from neighboring countries. Trucks that once sped across the German-Polish border have been sitting...