The center of Paris is Notre Dame.
This is true both literally and figuratively. The Gothic cathedral is there on Île de la Cité, the island in the Seine in between Paris' Left and Right banks, convenient and inescapable for the estimated 13 million people who visit it every year. Just outside, a Point Zero marker measures the distance to everything else in France. And Notre Dame is there in more than 850 years of French history: in paintings, daguerreotypes, songs, novels, war photos, awed selfies.