This is "The Three Shades," in the Rodin Museum in Paris. My question is why it was installed so that the Eiffel Tower is sticking up through the middle shade. The placement is obviously deliberate, but why? Is it meant to convey something? Did it just seem funny to someone? Or what?

Probably just happenstance coupled with touristic hyper-awareness. If you live in Paris you are generally not conscious of the tower unless you have a reason to be.
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Didn't you comment recently that the Eiffel Tower photobombs just about everything? There's your answer.
Given that the Tower and the statue seemed to be constructed in around the same time span, maybe it was thought that the Eiffel Tower, so hated by Parisians, would soon be torn down?
Evidently, the three shades were to "welcome" souls into Hell. Something out of Dante?
It’s throwin’ shade on the three shades! Hahahaha
Oh, look, there's the Eiffel Tower right there in the middle!
I adore the Eiffel Tower and have stood upon its heights, yet the reaction of many artists and Parisians was quite vitriolic in its day. I am writing a 'sorta memoir' about a time I worked briefly as a lowly construction laborer in Paris with the tower off in the far distance. I have researched some of that vitriol for the book:
“We shall see spreading like an ink stain the odious shadow of this odious column of bolted metal.” _~ from the article "Protest against the Tower of Monsieur Eiffel," 1887
And these reactions: “This truly tragic street lamp …” (Léon Bloy).| “This giant ungainly skeleton …” (Maupassant). | “A hole-riddled suppository …” (Joris-Karl Huysmans).
Maybe look at it from one of the other three sides?
Lol!
Looks like the shrubbery was due for a trim.