Here are my suggestions for obscure and dubiously-relevant mathematical
sites of interest in Paris.
First, aerodynamics. Our Brazilian colleagues will insist you see sites
associated with Santos-Dumont.
Second, cryptography. Paris was home to several celebrated cryptographers,
Rossignol, who worked for Louis XIII and XIV (i.e. Richelieu and Mazarin).
He worked either from "a room next to the King's study in Versailles" or
from his estate at Juvisy near Paris.
Bazeries (1846-1931), much of whose working life was spent at the Bureau
de Chiffre of the Ministry of Foreign Affairs, at the Quai d'Orsay (all
info from Kahn, The Codebreakers)
Third, structural engineering. The Eiffel Tower, or anything built by
Eiffel. He applied mathematics to determine how to make a relatively
small amount of metal withstand considerable stress. Look at the Eiffel
Tower to see how something so sheer can remain standing.
Fourth, astronomy. Once the Arabs brought Ptolemaic and their own
astronomy to Europe, the University of Paris became one the leading
centers of astronomy in the world, and remained so at least through
Laplace and Leverrier. Note that until the introduction of the
spectroscope, astronomy was a branch of geometry. Yes, astronomy was
mostly celestial mechanics (which the science-fiction writer Poul
Anderson defined as "angels in dirty robes with wrenches sticking out
of their pockets").
Speaking of science fiction, it was the Paris Observatory I believe
which computed the escape velocity from the earth at the request of
Jules Verne, who was then writing De La Terre A La Lune.
It may no longer exist, but look for the studio of the pioneering
photographer Nadar (whose friend Jules Verne shot him off to the moon
in De La Terre A La Lune).
Architecture, and the "arch" part is significant. Go to the cathedral
Notre-Dame, no not the front, which is mathematically uninspired, but
the Gothic arches and the flying buttresses. Then look at the other
extreme in stone arches, namely the Pont Royal and the Pont de la
Concorde with their elliptical arches.
Finally, be sure to ask your tour guide what train to catch for Nancago.
P.S. Not mathematically related, but be sure to visit the Opera and ask
the people there to see the underground chamber where the Phantom lived.