May sound odd, but if the Eiffel Tower, got LED lights (less watts for same brightness) instead of lightbulbs, and install solar panels

- on some of the beams of the Eiffel Tower structure, to collect electricity during the day to use at night
- somewhere in the nearby streets, to collect sunlight during the day and city-light during the night :D
- and if there are elevators, have a dynamo attached to the cable system so that the energy of the moving cabin, and movement of the cables, generates electricity (this was seen in an article about the newest energy-saving building designs).

Then it would save even more energy, because it likely won't need any electricity supply anymore.