The question is rather aimless, since the Eiffel Tower is of absolutely no help in
getting to the moon, and it's doubtful that several of them would be any more
effective than the single existing one is in that regard.
Nothing you could build from the ground in Paris could reach the moon, no matter
how high you build it, because the moon is never 48 degrees north of the equator.
You'd have to ship all of your steel and start stacking it somewhere within about
5 degrees of the equator. French Guiana, on the northeast coast of South America,
would be a good choice . . . you already have a space-launch complex there, and
a lot of French-speaking engineers.
The antenna spire of the Eiffel Tower is 324 meters (1,063 feet) above street level.
In order for your structure to just brush the moon, you would have to weld together
1,182,172 Eiffel Towers, tip to base.
The whole thing would probably need to be reinforced somehow. In order for it to rotate
every 24 hours, the outer tip would have to move at a little over 62,000 miles per hour !
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