Well, I thought that everyday, when the night is dark, the Eiffel Tower remained lit until sunrise. I recently found out by chance that all the tower lights are switched off at 1:00am.
But the most amazing is that the sparkling ( which usually occurs every hour for five minutes) remains active at 1:00am. The result is an incredible quick show at 1:00 am, when the tower becomes totally dark and sparkles in the total darkness.
Some examples here :