The most complete study in English of Fréchet's work that I know of is a series of three long papers (total of 217 pages) by Angus Ellis Taylor that were published in the 1980s:
A study of Maurice Fréchet: I. His early work on point set theory and the theory of functionals, Archive for History of Exact Sciences 27 #3 (1982), 233-295.
A study of Maurice Fréchet: II. Mainly about his work on general topology, 1909–1928, Archive for History of Exact Sciences 34 #4 (1985), 279-380.
A study of Maurice Fréchet: III. Fréchet as analyst, 1909–1930, Archive for History of Exact Sciences 37 #1 (1987), 25-76.
Near the top of p. 256 of the first paper Taylor writes:
In a number of theorems Fréchet deals with $V$-classes that are complete and separable. He calls them normal. This terminology has not survived; in later developments of abstract topology the word normal is given an entirely different meaning.