The Grothendieck Circle site suggests a more innocent explanation for the loss these letters.
Having left Montpellier in 1984....
In May of that year  a
secretary informed him that his office on the fourth floor of the institute had
been cleared out. Seeing this incident as an egregious example of the general
decline of mores, an outraged ...
You can find the quote (or something similar) in multiple places in the Théorie analytique de la chaleur, for example in
paragraph (article) 14:
"L'examen de cette condition fait connaître que l'on peut développer en séries convergentes, ou exprimer par des intégrales définies, les fonctions qui ne sont point assujéties à une loi constante, et ...
I think the conclusion here is that there is no proof that the claimed Fourier quote is an actual Fourier quote (in any language). However,
(1) Absence of proof is not proof of absence.
(2) Although Fourier may have not communicated the quote in substance, he did arguably communicate the quote in essence.
Possibly what happened was that someone wrote a ...