Blacklight Retribution, google it to find out what it is about.
It's a F2P game, and it's not P2W (seriously, I don't pay a dime and I have been playing it since March or so, and I have bought and unlocked most weapons by now), and it's greatly working out.
They have a GP and ZEN currency. GP is got by just playing the game, ZEN is got by paying real money.
And although the player levels range from 1 to 35 atm, a level 1 is still able to own a level 35 as things are incredibly balanced, and most of the time you cannot tell who pays and who's playing for free (generally you only know who pays by their player skins, if they have one only available by ZEN, then...).
So, a F2P without P2W and still being profitable is possible, each game just has to find its way to the best balance.