IMHO, "file group" is ok, as snailboat has written above (and "group of files" too).
When a noun is used to pre-modify another noun, taking on the role of an adjective (example: "chicken soup"), it is called noun adjunct or attributive noun (Wikipedia).
It seems that in highly specialized texts - technical or legal etc. - attributive nouns may be used in the plural. A quote (Wikisource; the article in Wikipedia also treats the issue):
As you know, Mr. Snowden has been charged with theft of government
property (in violation of Title 18, United States Code, Section 641),
unauthorized communication of national defense information (in
violation of Title 18, United States Code, Section 793(d)), and
willful communication of classified communications intelligence
information to an unauthorized person (in violation of Title 18,
United States Code, Section 798(a)(3)). According to news reports and information
provided by your government, Mr. Snowden is currently in the transit
zone of the Sheremetyevo Airport.
Maybe the quote is off the mark.. as I understand it, here we see several attributive nouns heaped before the head noun.