American soldiers in uniforms spill out from the bars and cafes all around June 6 Square, drinking beer and smoking cigarettes. Is this really France? “This is the 53rd state,” Philippe Nekrassoff, a local deputy mayor, said as he made his way across the square, with its Roman milestone and medieval church, while U.S. paratroopers wearing maroon berets played soccer with a group of local teenagers. “Americans are at home here.” Here is Ste.-Mère-Église, a slip of a town in northwest Normandy with one main street. About 3,000 residents live in the town and its surrounding region, with its fields...