All the strings in the language are enumerated whether it is RE or NOT RE.
Every language can be enumerated because language has finite length strings. And if i start from smallest string in the language and move to the next greater length and so on.Then i can map all the strings to the Natural numbers.For e.g if there is any two length and three length string in language ,then no other length string can come in between.As all the string length is discrete so it is possible to map it to natural numbers.
Hence every language whether it is RE or not ,it is always countable.So the statement is false.
Not RE will always be countable infinite.
Why not finite? Because finite is regular
Why not uncountable? As every language is countable.
Hence,given statement is false