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"}