Alright, I did some sciencing and it works now. As LiMZ said, renaming the folder to AionEu solves the problem -- except if you're using Steam. Here is what I had to do if you have Steam and you want to fix this right now. Basically, if you were wondering if it would work if you just replaced the language files with the proper ones then the answer is yes, it does work. Still, here are the step by step instructions.
1) Copy C:\Program Files\Steam\steamapps\common\aion to C:\Program Files\NCSoft and name it AionEu (C:\Program Files\NCSoft\AionEu).
2) Open C:\Program Files\NCSoft\Launcher\NCLauncher.exe
3) You will notice you now have two Aions on your launcher. Open the one under (the one that doesn't say North America) and let it update. When it's done, close it.
4) Copy C:\Program Files\NCSoft\AionEu\L10N to C:\Program Files\Steam\steamapps\common\aion and replace the folder of the same name. You can now delete C:\Program Files\NCSoft\AionEu since you don't really need two copies of Aion in your computer.
5) Open the launcher again through Steam or through wherever and launch the game. It should be in English. Also the Steam Overlay finally works with this patch.
6) Do a little dance because it now works.