This link contains excerpts of Fourier's descriptions of some of his math professors but doesn't really provide any source. What's the name of the original document containing these descriptions?
As GEP as asked for a translation into english of some parts of the Gallica text, here it is :
"I have noticed Cousin, Lallande, Brisson, librarian Pancouke, some teachers from the Lycée. Some of them are dropped by national carriages or with representatives : no teachers come in another way. Here are some details about the professors : these tiny details will look superfluous, but I write them because you don't find them reported in newspapers. Lagrange, the first among european scientists, looks between 50 and 60, although he is younger : his face testifies dignity and refinement : he looks rather thin and pale ; his voice is very low, unless he gets angry ; he has a very strong italian accent and pronounces "s" like "z" ; he is dressed very modestly in black or brown ; he speaks in a very straightforward manner, somewhat with difficulty; he has in his speech the embarassment and simplicity of a child. Everybody sees he is an extraordinary man, but you must have seen him to recognize him as such. He speaks only in conferences and some of his sentences are laughable : "there remains on this subject many important things to say, but I will not say them". The students, most of them unable to appreciate him, do not especially welcome him, but the professors do it in counterpart. Laplace, who has as well a chair of professor of Analysis, had been appointed in the Melun school, he had accepted it ; the government has repeared this administrative error. Laplace is first rank among scholars, he is known all over Europe as an excellent geometer, physicist and chemist. He looks rather young, has a little voice, though clear, he speaks with precision, albeit with some difficulty ; his exterior appearance is rather nice ; he has a very simple clothing ; his height is in the average. His mathematical teaching, by no way extraordinary, is given at a very fast pace. Haüy, who has been formerly a priest, is extraordinarily simple and modest; he isn't old, his clothes are almost that of a clergyman ; moreover he has refused to swear [the civil constitution of the clergy]. His voice is very clear, very audible, and he speaks with much elegance and easiness. It is impossible to speak better. Some say that he memorizes his lessons ; it is said that he reads a part, something that is difficult to check because the professors are far away and always have their lecture notes in front of them. He is so shy that if somebody in the audience asks for some precision, he gets confused, answers in a wrong way or do not answer. He has a wide knowledge, and, though not as brilliant, without the genius of the first two, he is shining by his method and the way he provides the most elegant proofs."
I will probably add his opinion on Monge in the near future.
On pp. 3-4 of  Grattan-Guinness writes:
The professors were drawn from among the foremost men in the land: for example, [Lagrange, Laplace, Monge are mentioned] $[\ldots]$ The school opened on 20 January 1795, but lasted only a few months. The failure was partly due to the severity of the winter weather, which caused the already impoverished students to live under conditions of great physical hardship; but there were other difficulties, caused by the poor organization of the teaching. Fourier himself described some of them in a letter $[\dots]$ Both Lagrange and Laplace were quiet speakers, with Lagrange outstanding for his Italian accent and Laplace for the rapidity of his teaching $[\dots]$ Monge caught Fourier's imagination, speaking with a loud voice and showing great skill in both theoretical and practical subjects.$^6$
Footnote $^6$ (bottom of p. 4) begins with: "Undated letter to Bonard, in A. Challe 1858a, 115−120; also in E. Duché 1871a, 257−261. [$\ldots]$" As with pretty much anything before 1900, these two references are freely available on the internet (see  and ). These two references are in French, so for me it would be difficult to determine whether the precise MacTutor History of Mathematics archive quotes are there, and if so, where, but perhaps someone else who can easily read French can comment further.
 Ivor Grattan-Guinness, Joseph Fourier 1768−1830, in collaboration with Jerome Raymond Ravetz, MIT Press, 1972, xii + 516 pages.
 Ambroise Challe, Lettres de Joseph Fourier [Letters from Joseph Fourier], Bulletin de la Société des Sciences Historiques et Naturelles de l’Yonne (1) 12 (1858), 105-134. (google books version and Gallica version).
 Émile Duché, Joseph Fourier, sa vie et ses travaux [Joseph Fourier, his life and his works], Bulletin de la Société des Sciences Historiques et Naturelles de l’Yonne (2) 5 (1871), 217-262. [see pp. 257-261] (google books version and Gallica version)