La tour Eiffel. The Eiffel tower. The most visited paid monument in the world. In a country of iconic buildings this one is likely the most iconic.
Named after its creator Gustave Eiffel. The same guy who in 1886 hammered out the Statue of liberty. In 1889 he got busy again and the tower was built as the entrance to the 1889 worlds fair. It's still the tallest structure in Paris at 1,050 ft (360m) in its day it was the tallest man made structure in the world. A title it held for 41 years until the Chrysler building in New York was built. However, eventually the French added some radio towers to the Eiffel and now it's taller than the Chrysler building (take that!).
Over its life it's been more than just a monument and radio tower. It has also been (and is) a beacon for aircraft, home of a resaurant and a nifty place for which to park your Zepplin.
Fun Fact: In World War II when Hilter was occupying France, even though he wanted to, he was never able to go up the tower as mysteriously the elevators never worked while the Germans were in Paris. Oddly enough the day the allies liberated the city by the seine those lifts started working again just fine thank you very much. Its all part of that selective French hospitality I suppose.