From this page:
The adjective "Ashkenazic" and corresponding nouns, Ashkenazi
(singular) and Ashkenazim (plural) are derived from the Hebrew word
"Ashkenaz," which is used to refer to Germany.
...I searched the literature for confirmation and found there were two camps:
(Opinions which agree with the above):
Dovid Katz, Yiddish and Power (here): Ashkenaz=name of an ancient civilization; Ashkenazim=people; Ashkenazi=a person; Ashkenazic=adjective
The New York Times Manual of Style and Usage (here): "Ashkenazi is the term for a Jew who settled in middle or northern Europe after the Diaspora, or that Jew's descendant. The plural is Ashkenazim, and the adjective is Ashkenazic."
(I consider these variant [identical] opinions):
Leo Rosten, The New Joys of Yiddish: Completely Updated says (here): "'Ashkenazic' is an English adaptation of 'Ashkenazi' [i.e., implying that both are adjectives --SAH]. [...] [From] Hebrew: Ashkenaz, 'Germany.'" --...But, separately, he lists "Ashkenazi/Ashkenazim (plural)/Ashkenazic (adjective)" [sic] as the three variants, implying that "Ashkenazi" is a singular noun. (The definition under this heading begins: "Ashkenazim and Sephardim are the two main branches of Jewry," which seems to confirm this interpretation.)
--In short, Leo Rosten thinks "Ashkenazi" is an adjective and/or a singular noun for a person; "Ashkenazim" is a plural noun for people; "Ashkenaz" is a place; and "Ashkenazic" is another adjective.
Sol Steinmetz, Dictionary of Jewish Usage: A Guide to the Use of Jewish Terms, p. 11, thinks the same: "The name ['Ashkenazi'] is also used as an adjective, along with Ashkenazic, as in Ashkenazi (or Ashkenazic) Jews, the Ashkenazi (or Ashkenazic) Hebrew pronunciation."