It would make a fine billboard. In fact, it already has. In the late 1920s and early 1930s, three of its sides held vast advertisements for Citroen cars. While occupying Paris during World War II, German troops hung a sign from the tower trumpeting their victory. In 1979, a Greenpeace protester unfurled a sign that said Save the Seals. A company called Apoteo Surprise will flash a personal message under the Eiffel Tower — for a price.