Hello !
The Eiffel Tower is considered in France as Monument Historique (Historical monument) only since the 24th of June 1964. In France, the Monuments Historiques are a very regulated category of buildings with a juridical status aimed at protecting them. There is 44 236 monuments historiques. This status is codified under the Code du Patrimoine (Code of Heritage). Source : https://www.legifrance.gouv.fr/affichCode.do?idArticle=LEGIARTI000029694828&idSectionTA=LEGISCTA000024241836&cidTexte=LEGITEXT000006074236&dateTexte=20160915
Additional laws since then strictly forbid advertisement on Monuments Historiques. The Code of Environment, its Article L581-4 says :
« I. - Toute publicité est interdite : 1° Sur les immeubles classés ou inscrits au titre des monuments historiques ; »
Translation :
I – All advertisement is prohibited : 1°On buildings classified or registered as historical monuments.”
And since the 1979 Law on Advertisement, this prohibition was absolute for Monuments Historiques, no derogation is possible as part of a local, in this case Parisian, regulation on advertisement .
Source : https://www.legifrance.gouv.fr/affichTexte.do?cidTexte=JORFTEXT000000705047
However since 2006, it is possible to put advertisement on Monuments Historiques with three conditions :
° Scafolding must hide exterior works. (Art. R 621-86 du code du Patrimoine) ° The earnings must be used to finance the works (Article L621-29-8 du Code du Patrimoine) ° The ad must not cover more than 50% of the working area. (Art. R 621-90 du code du Patrimoine)
Usually it means the company advertising on a monument is participating to its renovation. It was the case for the Palace of Versailles, where the company Vinci (construction) had large billboard on it, but payed for some of the works.
This law has proved very controversial in France, during the renovation of the Grand Palais in 2008, or at the Musée d’Orsay in 2011, and many more cases. Apple had a huge ad on the Place des Vosges in the heart of Paris. And so on. Here’s an example of the Conciergerie with a Dior ad :
To answer your question, no advertisement is possible on the Eiffel Tower, unless if it underwent major renovation, with the limitations mentioned above.
Ps : And thank god it's a sturdy construction and probably won’t need renovation before a long time.