Strolling in bright sunshine across the immaculately raked gravel of Paris's Tuileries gardens, Barbara and Rick Wilson from Dallas, Oregon, were not exactly in disguise. But earlier that morning, on their very first trip to France, Rick, 74, had taken an unusual precaution. Before leaving his hotel, he'd taken a small piece of black tape and covered up the Stars and Stripes flag on the corner of his baseball cap. "We're sick about it. It's horrible. Just horrible," said Rick, as he and his wife contemplated the sudden sense of shame and embarrassment they said they now felt, as Americans,...