No FPS in EVE online as far as I know. The only thing that could drag me into a space MMO is a mix between space exploration and fps combat. That's why I loved ME1 so much, despite it's relative simplicity on that matter.
Also, the EVE community has created quite a bit or arseholes (see #1). I already have problems wrapping my mind around the idea I'm breathing the same air as that....thing. Like hell I'm gonna play the same game as it.
...Elite: Dangerous seems an interesting prospect, thou.
Eve really is something you'll either love with a passion or hate. Its depth is unrivaled and learning curve can be very overwhelming to say the least. Its a game that I tried in the past but wasn't mentally prepared for so I wrote it off and tried to forget about it. Then I'd hear stories about something that happened and it would just captivate me. Surely, if reading about these truly EPIC events and a real working player based economy that actually makes sense is interesting, then maybe Eve is worth the steep learning curve and griefers.
Finally after a few failed TRIAL ACCOUNT attempts, I decided after the constant disappointment from countless PC titles to really give it a dedicated attempt. Best decision EVER! Eve is actually an extremely deep and complex quality game though it does have some seriously questionable people playing it. Its really the only MMO that has been sub based for the last 10 yrs other then WoW and it numbers are still very very strong. New players are starting everyday regardless of the extreme advantage 10yr vets have.
I wrote all this because I really wish I would have given it a better more honest effort many years ago when I first tried it but I heard many negative things about its community and learning curve due to its extreme depth.
Though be warned, its certainly not like most games, it's called spreadsheet simulator for a reason