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.