User 'Hassle12' over at NexusMods has put together an easy to install texture overhaul that noticeably cleans up and enhances the textures, making playing on HD displays all the more enjoyable.
Screenshot comparisons by the author posted below.

This also pairs well with the Setting higher resolution and getting widescreen support + Mouse Fix and How to make the visuals better. + High refresh rate fix guides, but are optional in the event you've started playing in the original 4:3 resolutions.

►DOWNLOAD HERE◄

Installation:

Originally posted by Hassle12 on NexusMods:

Unpack "textures" and "system" into Your XIII Classic main folder. For steam by default it's C:\Program Files (x86)\Steam\steamapps\common\XIII - Classic
Screenshots folder includes some comparison material before and after.

As of version 1.1 everything should work properly. If You found any bug I missed feel free to leave feedback :) Have fun!

Please leave bug feedback on the NexusMods page and not here. I take no responsibility for the creation of this mod. 100% of the credit goes to Hassle12. This guide is only here as a promotion to the original author's creation.