UPDATE 2021-06-06:

Japanese audio is now also supported.

UPDATE 2021-02-26:

For those who would like to get a better idea of the difference in quality without having to download the full mod, I added some sample audio snippets to the miscellaneous files download section.
These samples are just from random early-game cutscenes and not cherry picked worstcase scenarios. You could probably find many clips were the difference is even more staggering if you went through all the cutscenes.

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README
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You can use these audio tracks either with:
a) Original cutscenes
b) Full hd cutscenes from this or this mod

In case a), the audio tracks are only replaced in copies of the movie files. This means you need ~20GB of additional space (per language), but it will be easy to uninstall/toggle this mod.
In case b), the audio tracks of the full hd cutscenes are directly replaced without a backup (since those videos already consume >90 GB per language). If you want to be able to go back to the full hd cutscenes with vanilla audio quality (or to be safe in case something goes wrong), you should manually create a backup of your 'FINAL FANTASY XIII\white_data\movie' folder before proceeding with the installation.

DISCLAIMER: There may be bugs, use at your own risk.

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Prerequisites:
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• Install RAD Video Tools from here
• Install Python 3 on your System
  • on Windows 10 you can simply install Python 3.9 from the Windows Store
  • alternatively, you can download the latest 64-bit Python version from here (Important: Make sure to tick the box Add Python to PATH during installation)
    
  
  

To verify whether Python was installed correctly:
Open a cmd window (e.g. via win+r, type cmd, enter) and enter the command:
python --version

-> this should display the version number.
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Install:
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• Download the Audio Tracks for your desired voice language(s) (English, Japanese or both) and the latest patcher from this mod's download page and extract the contents of both archives into your 'FINAL FANTASY XIII\white_data\movie' folder using 7zip.
  
  
  After this step, you should have the following additional files and folders in your movie folder:
  ps3_audio\  (English files)
ps3_audio_jp\ (Japanese files)
audio_replacer.py
audio_replacer.cmd

• Right click audio_replacer.cmd and run as administrator. Follow the instructions. Whenever the tool prompts for your input, type your answer and confirm it by pressing <enter>.
  The patching will take a while once it starts. It's finished when you see the message "Done!".
• (Optional) To save space, you can now remove the ps3_audio/ps3_audio_jp folder or move it somewhere else (it is only needed during installation).
  

IMPORTANT: If you are NOT using the Full HD FMV mod, some additional steps are required to make the game load the patched cutscenes instead of the original ones:

• Download the main program v1.0.5 (~300kb) of GreenThumb2's English Full HD FMV mod from his mod download page and extract it into any folder
• Double click _Install_HD_Movies_English.bat or _Install_HD_Movies_Japanese.bat depending on your desired voice language (if you want both languages, simply repeat steps 2-4 for the other file after you are done).
• When asked, pick "Install HD (M)ovies" (type M, then enter)
• When asked, select "(A)dd new ones" (type A, then enter)
  

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Uninstall
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• Depending on what you chose during installation double click either _Install_HD_Movies_English.bat / _Install_HD_Movies_Japanese.bat (from the full hd movie mod main program, this should already be somewhere on your drive, either because you installed the full hd mod or because you followed the steps from the second block of the install instructions).
• When asked, pick "(O)riginal ones" (this will also uninstall the full hd cutscenes if you are using them!)
  

(Optional) If you want to completely erase the modified video files to free up space (WARNING: will remove full hd cutscenes if installed, also make sure that the original cutscenes with bad audio are working in game before doing this):

• Open an explorer window and go to "Final Fantasy XIII\white_data\movie"
• In the search box, type "z*_*_us.win32.wmp size:>1mb" (English FMVs) or "z*_*.wmp size:>1mb NOT *_us*" (Japanese FMVs)  (in both cases without the "), and delete the 106 video files which should be displayed.