How to check a String if it's an ASCII or not?

There is a bult-in Ruby string method right for you.

str.ascii_only? # → true or false

Returns true for a string which has only ASCII characters.

"abc".force_encoding("UTF-8").ascii_only?          #=> true
"abc\u{6666}".force_encoding("UTF-8").ascii_only?  #=> false

If your strings are Unicode (and they really should be, nowadays), you can simply check that all code points are 127 or less. The bottom 128 code points of Unicode are ASCII.