Regular Expressions 101

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/
^(?:[\u0000-\u007F]+|[\u0370-\u03FF]+)$
/
gm
^ asserts position at start of a line
Non-capturing group
(?:[\u0000-\u007F]+|[\u0370-\u03FF]+)
1st Alternative
[\u0000-\u007F]+
Match a single character present in the list below
[\u0000-\u007F]
+ matches the previous token between one and unlimited times, as many times as possible, giving back as needed (greedy)
\u0000-\u007F matches a single character in the range between (index 0) and  (index 127) (case sensitive)
2nd Alternative
[\u0370-\u03FF]+
Match a single character present in the list below
[\u0370-\u03FF]
+ matches the previous token between one and unlimited times, as many times as possible, giving back as needed (greedy)
\u0370-\u03FF matches a single character in the range between Ͱ (index 880) and Ͽ (index 1023) (case sensitive)
$ asserts position at the end of a line
Global pattern flags
g modifier: global. All matches (don't return after first match)
m modifier: multi line. Causes ^ and $ to match the begin/end of each line (not only begin/end of string)
Your regular expression does not match the subject string.

Regular Expression
No Match

/
/
gm

Test String