In Battlefield 1's Alpha, you were able to extend the view of your weapon FOV as well as the world FOV. World FOV is what people think of when FOV is a setting for games. It affects your field of view in first person. While weapon FOV affects how close the guns look to your player's face. To use this mod, you simply have to open the .exe file, input a FOV setting and your setting will update in-game, only when in a match. Unfortunately, the FOV setting will reset after every match, so it will have to be manually updated each match. Personally, I find 70-75 to be the sweet spot, because a higher value may cause visual glitches. 

Original link to mod can be found here, and was created by "menready1108".

I want to stress that I did not make this mod, I only re-uploaded it.

This mod has no risk of getting you banned when playing online, since no fundamental gameplay values are changed.

UPDATE:

Included as an optional mod download, a new mod has been added that modifies weapon FOV values when aiming down sights. All sights are affected besides LMG AA sights and some optical sights. Currently the mod will increase the FOV of all weapons when in ADS. Some guns will have visual issues when aiming unfortunately. It is also recommended you turn "Weapon ADS DOF" to off ingame. Use the mod with Frosty Mod Manager.