I should be living proof that speaking other Latin based languages does not improve your English (anecdotal evidence). Mind you, English is my 3rd official language, and I still suck at it. I also started a little later in life (I was 20).
The biggest issue or challenge is spelling because English is an odd language that does not follow “you write what you hear”. Hence, spelling rules are a unique way of learing it, and I have been dealing with the limitation of my style of learning.
Moreover, English is easier than many other languages, and it makes it tougher to learn (that’s no joke). Let me share a great example, in English I heard fewer words than any other language I speak, and the word “GET/GOT” gave me the biggest challenge of all….I have over 20 unique meanings my native tongue, and I’m always limiting my use of certain “got ya” words.