Watch out after dark, at least if you are in Paris. Apparently, it is illegal to publish photos of the Eiffel Tower taken after dark without permission. Given the prevalence of photo books and other similar products this restriction seems extreme, but it exists nonetheless.
Apparently, in 2003 SNTE, which manages the tower, changed the lighting and then copyrighted the resulting image. SNTE was able to do this because French courts have upheld copyright based on the specific lighting. I doubt this trick would hold up in the U.S., but then the Eiffel Tower isn’t in the U.S.
For more details on this restriction see Eiffel Tower (Wikipedia), Eiffel Tower Repossessed, and Image Rights/The Eiffel Tower Brand.
The photo used to illustrate this article was taken in Las Vegas, so I’m not violating any laws.
All About Images Blog 
There is always the one in Vegas, from the right angle, it might look the same.
I don’t know where you got this information but I was just there and there were hundreds of thousands of people taking photographs of the Eiffel tower
Myself included
Marianne Jennings
The issue is not with taking photos but with publishing them, which potentially includes photo books and other products. The links within my article give additional information on this restriction.