"In my opinion it is fine."
Translation:Według mnie jest dobrze.
The similarity between the two words can indicate, that they are cognates, but dictionaries say, they aren't (at least not direct): 'fajny' came to Polish language through Silesian dialect as a loan word from German (fein).
And 'fajny/fajnie' means more than good, dictionary says cool, nice, great. So I think it is not the same.
"Fajnie" is colloquiaI and I would translate it to English as "nice, cool" ("Fajnie wyglądasz"="You look nice", "Fajny samochód"="Cool car"). So the Polish "fajnie" and the English "fine" are not exactly the same word. You could say "Według mnie jest fajnie" (or maybe, "Jak dla mnie jest fajnie" - this construction sounds more natural since "jak dla mnie" is more spoken and less sophisticated than "według mnie") and the general meaning would be still the same ("In my opinion it is fine/alright/OK/cool"), but I guess the precise meaning and connotation is slightly different - maybe someone with a better intuition for English can comment on this?