???

Mirror's Edge has a female protagonist, but it's not an FPS (First Person Shooter). It's a parkour simulator which technically lets you shoot a gun in limited sections of the game, but the protagonist is a pacifist and you get a bonus for decommisioning guns rather than firing them.

If the thread would like some hard data:

- 19,526 games on Steam tagged "female protagonist" https://store.steampowered.com/search/?tags=7208&ndl=1

- 13,578 games on Steam tagged "FPS" https://store.steampowered.com/search/?tags=1663&ndl=1

- 727 games on Steam tagged both "female protagonist" and "FPS" https://store.steampowered.com/search/?tags=7208%2C1663&ndl=...

So it looks like the two categorisations, for the most part, don't intersect.

Notable counterexamples would include Rise of the Triad, Ion Fury, No One Lives Forever, Wolfenstein: Youngblood and Far Cry 6, but definitely rare. You'd be clutching at straws to describe Portal or Alien: Isolation as FPS (they're a puzzle game and survival horror game respectively), likewise the Resident Evil / Clock Tower / Fatal Frame / etc. games with the novelty option of switching to first-person view, they're naturally third-person perspective. Left 4 Dead has one female character out of four you can play. You might count that one DLC for Bioshock: Infinite where Elizabeth gets a shot (https://www.youtube.com/watch?v=1E1lh-pb6Is). You might count the few FPS RPGs that there are with customisable characters (so yes Fallout, but not Mass Effect as it's third-person). But female protagonists are massively more prevalent in survival horror, metroidvania, third-person shooters (Tomb Raider, Monster Hunter, Horizon Zero Dawn, etc) and other genres besides FPS.