Download Flawless Widescreen[flawlesswidescreen.org] which is a general FOV mod program that features fixes for a variety of different games. With the program open, scroll down the plugin list on the left to find LEGO SW: Skywalker Saga and click on it. It should download and move to the top of the list under Installed Plugins automatically. Select it and configure to your liking. I recommend turning all the Individual Fixes except the FOV Fix off unless you're using an ultrawide monitor, since they can cause various visual glitches and serve no purpose on standard 16:9 displays anyway.

And that's it! As long as the "Fix Enabled" checkbox is checked, it will automatically apply the fix when both Flawless Widescreen and the game are running.

You may experience a few minor visual glitches while using Flawless Widescreen with this game, but nothing that should get in the way of the experience. You can always alt+tab and disable the mod temporarily if necessary.

The Flawless Widescreen plugin allows you to increase the FOV by a percentage rather than specifying an exact value, since it adjusts multiple different FOV values. The game's default (vertical!) FOV is 48.7° vertical, or somewhere in the range of 76-77° horizontal on a 16:9 display.
Setting the FOV adjustment to +21% gives you about 59°, which translates to a standard horizontal FOV of 90° on a typical 16:9 display. This should be a good value for most people, but you can increase it higher if you like. I also turned the Max FOV slider down to 70 since I thought that sprinting was widening the FOV a bit too much.

Default FOV left, my recommended +21% FOV right:

I hope this guide helps some of the many people who have complained about this game's low FOV since its release. If there is ever another game update, the mod will likely need to be updated to support it so please be patient.