Some games will force the player to have a fixed aspect ratio, other games will allow a dynamic aspect ratio.
This is something you need to decide first. Fps games that Im aware of have very low FOV values for 45-90 (90 being very high with modern widescreen monitors). if you want to want to take full advantage of widescreens then try use a small fov. This is a scenario where only testing the application at all sizes will allow you to determine what works best.
with older monitors 90 fov wasnt such a big issue, QuakeWorld had 90, and I would often turn it up on my old CRT. That's because screen resolution increases where usually always close to the same ratio, and most old games couldn't be resized.
So I would recommend developing your game at a FOV like 45, and resizing the screen to extremely wide view when making changes. no fixed aspect ratio means develop and test, develop and test. Once you are ready to release you can increase the fov to something like 60 as a default
The other issue you will face with screen resizing is the 2D ortho issues of having all the text in the screen. If a sentence can be viewed in widescreen once you resize it to portrait view, it may get squished and look silly. If you dont want it to squish, only half of it will appear. There is a few different solutions for this, though