To be honest, I couldn't tell if it is accepted or not.

I think it is, but we simply don't see it that often. As far as I can tell, it is perfectly correct to abbreviate in the english language.

http://www.encyclopedia.com/doc/1O25-fe.html

No, f.e. is not an accepted or known abbreviation, it's not perfectly correct. You can try and start one, after all yolo, lol, rotfl. Or perhaps not ;)

When I asked, I was wondering if it was a known abbreviation from an academic field I didn't know. I wouldn't use it, e.g. is the correct abbreviation to use in this instance.

Interesting. Most references that I found say that f.e. is not correct. ;)