Frequency analysis secure language Let’s say there’s a language that has all the letters of the alphabet evenly distributed.

Is this language then secure against frequency-analysis or could there still be some soft of weakness, i.e. by using too short keys?
Substitution cipher (e.g., Caesar) and polyalphabetic substitution cipher (e.g., Vigenere) are deterministic encryption schemes. The same plaintext will always result in the same ciphertext. So, they are not secure in the sense of indistinguishability under chosen plaintext attack (IND-CPA).

It may be possible that "all the letters of the alphabet are evenly distributed", but it is very unlikely that all the 2-grams, 3-grams, etc., are evenly distributed (because some of them may be meaningless in the language). In this case, the frequency analysis can still work.