For an English translation of "J'aime le soleil", could one say, "I like sun" as in a general sense, thus omitting the article?
No, because French uses the indefinite and definite articles that English omits
They are inconsistent with translations of the article. I like fog is accepted but I like sun isn't. It seems to be guesswork whether it should be there or not, but generally both are acceptable in English with very slight nuances of meaning apparently not expressed in French which always uses it.
Okay, so that's three of us saying "sunshine". I don't know--maybe there's a separate word that better captures the sense of "sunshine" as distinct from "sun". But I'm pretty sure if I had to translate this for someone, I'd say I like sunshine, because "I like the sun" or "I like sun" both sound, well, unnatural.
In English, I like the Sun can mean two things. It can be short/sort of slang for I like sunshine. Or, more correctly, it means that you like the star that warms and lights, etc, our Planet. Hmm.