Hi,
A lot of paranoid and uninformed prognostications here... It seems the subject was already beaten in another thread, but well... let's go.
@Ces1um : You (and me) have completely the right to photography the Eiffel Tower, during the day, without restriction.
When the lighting is in use (i.e, during the night), yes, this lighting is copyrighted as can be a work of Art (I am not discussing the validity of this assertion here - to me, as an astronomer, it's essentially light pollution

), and is protected as Intellectual Property.
This copyright prevents you to use your photos of the illuminated Eiffel Tower in a *COMMERCIAL OR PROFESSIONAL USE*, or to publish without permissions, and should give eventually royalties to the rights owner, which is "Société d'Exploitation de la Tour Eiffel" and the creator (Pierre Bideau).
So, unless if you plan to takes photo, makes a zillion of postal cards with them, and SELL them, you risk absolutely nothing, with a private, non-profit use.
There is however a subtlety concerning the publication right, coming with anyone publishing anything on internet, instead of printing it in a book or magazine :
Yes, posting a night illuminated Eiffel tower on Facebook or Instagram can be considered probably as a publication.
In reality, to my knowledge, the number of people who get sued or even just worried about a "published" night photo with Eiffel tower on the Net, is probably near Zero, nada, zilch.
If you want to be on the safe side, when "publishing" (for non -profit I insist) your photos, you can add the mention "Copyright SETE/Pierre Bideau" and then you can walk away with a spring in your step
Regards,
Raphael (from France)