This is a pretty ugly hack, but maybe it will inspire you to something better.

    leastCJK = ToCharacterCode["⺀"][[1]];
    StringMatchQ[#, _?(ToCharacterCode[#][[1]] < leastCJK &)] & /@ 
      {"a", "1", ".", " ", "中", "あ"}
>     {True, True, True, True, False, False}

Note: "⺀" is unicode character U+2E80, CJK RADICAL REPEAT

This hack can be with `Repeat` to ignore CJK strings

    StringCases[
      "the quick fox...んは本当に日本語を勉強していますか...jumped", 
      Repeated[_?(ToCharacterCode[#][[1]] < leastCJK &)], 
      Overlaps -> False]
>     {"the quick fox...", "...jumped"}