The Eiffel Tower has undoubtedly become the iconic romantic place in the world. Thousands of people propose and get proposed to in front of the Eiffel Tower every day, but that doesn't make it any less romantic.
The Champ de Mars, which is the green pasture under the Eiffel Tower, is often the most popular choice. However, it is usually crowded and busy, and not really a good idea if you want a flawless picture of your proposal with no one in the background. For a more secluded option, a better location is the small footbridge near the tower with its view, called Passerelle Debilly. The Pont de Bir-Hakeim, with the metro rail running above and a few pedestrians alongside, also has a distant but a very romantic view of the Eiffel Tower.