Mathematica, 46 bytes
====

    Count[Characters@#,c_/;RemoveDiacritics@c!=c]&

To be honest, I do not really understand the description :P, but the function just works.

Test cases:

    f=%; (* assign the function to f. *)
    
    f["Zoë reads the encyclopædia in a café"]
    (* 3 *)
    f["Zoe reads the encyclopaedia in a cafe"]
    (* 0 *)
    f["Zoë"]
    (* 1 *)
    f["Zoë"]
    (* 1 *)
    f["déjà vu"]
    (* 2 *)