“Very” fun is not English. I would suggest “great” fun.
It depends on which dialect you speak. It’s correct in English from the Midwestern US.
Just because people in the midwestern US say “very fun” doesn’t mean it’s correct English. But if you want to say that, good luck to you.
There is an interesting reference to this made on the English Wiktionary article for fun. The article makes a note about the adjectival use of “fun” and states -
Note that, prescriptively, the adjectival use of fun, instead of funny as in a funny movie, is often considered unacceptable in formal contexts. This includes censure of the comparative and superlative funner and funnest, but equally constructions such as very fun (rather than, say, a lot of fun). For more, see Quinion’s discussion.
Speaking for myself, I certainly wouldn’t say “very fun”, or “funner” or “funnest”, and if one of my native English speaker friends said one of those words then I’m sure that I would find it a little strange.
However, since we don’t have a formal language body for English, then as times change the idea of what might be considered correct or incorrect English (particularly in informal contexts) can be a little open to interpretation.
That’s what dialects are about. I don’t think any region is more “correct” than another, but maybe it’s because I’m more of a descriptivist. There’s about 69 million Midwesterners, so it’s not some small population that says it this way. If I were to hear someone where I live say, “That was great fun,” I’d be a bit taken aback; it sounds unnatural to us. That’s the beauty of languages, though. It evolves. And maybe using “fun” in that way was incorrect historically, but it’s become correct in my dialect.