OMAHA BEACH, France—Jim Kosinski sensed something was wrong when he noticed the American flag wasn't flying here on this windswept shoreline, the final resting ground of thousands of U.S. troops who died during World War II's D-Day invasion.

Moments later, the 71-year-old military veteran—who traveled from Ventura, Calif., with his wife to pay homage to the fallen soldiers—saw the sign affixed to the cemetery gate: "Due to the U.S. Government shutdown this site is closed to the public.

"How embarrassing," he said. "Our flag wasn't flying over our soldiers who gave their lives."

The shutdown of the federal government and the subsequent closure of national parks and monuments across the U.S. have forced people to cancel vacations and reschedule weddings. But few visitors to the blustery coastline of northwestern France—where more than 3,000 allied troops died in the first day of the battle to free Europe from the clutches of Nazi occupation—expected to feel the repercussions.

U.S. war memorials on foreign soil, however, answer to the federal government back in Washington. So when the shutdown took effect earlier this month, the Normandy cemeteries closed their gates as well.