You can try the following:
1. Xpadder
WARNING: You Must Pay For This Program.
You may purchase / acquire a copy of Xpadder, and remap the keyboard controls to a gamepad. During this process, when mapping the mouse to the right analog stick, you have the following options: Regular mouse, Inverted X, Inverted Y, and Inverted X+Y.
The gamepad I use for my PC is an old 'Madkatz' Xbox 360 wired controller, which has a Right Analog Y-axis inversion switch on the back that I use all the time. Having the hardware do the inversion for you is always the best solution, I've found.
That being said I tested the Xpadder method using the X axis inversion, and it does seem to work.
Do note, however: I have noticed other message boards / threads stating they installed an x inverter program, only to have it stop working randomly.
2. Joy 2 Key
Same basic function as Xpadder - this program maps keyboard and mouse input to a game pad. The Gui is extremely basic, and is much more difficult / annoying to set up. But it's free.
I did not bother to test this program after seeing the GUI.
3. Polynomial's Mouse Inverter - v1.0
File Location: sendspace.com/file/zjuwfv
I found this after a quick Google search. It was posted on a forum in which the original poster was looking for a way to completely flip a Mouse's X & Y axis' in windows for a client with severe dyslexia.
Requires Microsoft .NET framework 4.0 to run.
WARNING: This program will effect all mouse movement on the system after being enabled.
This program does allow you to chose which axis to invert upon start up.
However, it has been mentioned on the forums here on GoG, the Steam Forums, and elsewhere that Beyond Good and Evil will actively ignore this program's mouse inversion. I myself have had the program work properly once, subsequent uses of the program have caused windows file explorer to hang after running (Win7 x64).
Use at own risk.
4. Axis inverting or rotating mouse filter driver by MAF-Soft
Website: maf-soft.de/mafmouse/
WARNING: You Must Pay For This Program.
The website lists Beyond Good and Evil as #1 on it's "Hall of Shame". I assume this means it has been tested by the author to guarantee functionality. Since one would need to contact the software author for the price of the software, this question would best be asked during first contact.
I have not tried this software, and have no desire to do so.
5. AutoHotKey (AHK)
Website: autohotkey.com/board/topic/17828-invert-mouse-axis/
Of Note: autohotkey.com/board/topic/17828-invert-mouse-axis/page-2 - First entry
I found this entry in the Autohotkey community support forum. Opening post was asking how to invert the mouse axis of a 'mouse like device' the person fabricated themselves. However, the first entry of the second page has a script with 3 global Boolean variables to alter the mouse cursor's behavior: Swap_xy, Invert_x, and Invert_y.
Further entries on page 2 refine the script in various ways.
I have not tested this method in the slightest.
6. SakasaMouse
File Location: Download via CNet.com
This program is described as a 'joke program', and states it's purpose as mouse inversion. It is mentioned both on the Autohotkey site, and on the Steam Forums for Beyond Good and Evil. However, according to the Steam Forum thread, it is neither a global, nor reliable solution. Some reported it worked, only to come back saying it no longer worked. Some stated it did not work at all. One Steam Forum user went so far as to say the reason the program did not work is due to Beyond Good and Evil ignoring the system registry values for inverted x / y input.
Use at own risk.
I have not tested this program.
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Frankly, the options seem to be thus:
A) Get used to standard mouse input
B) Use a gamepad with either Xpadder or Joy2key.
C) Muck about with various software which may work, may randomly cease working at any time, or may incite changes that are ignored by the game upon launch.
Hope this helps.
-JJ
Post edited November 02, 2013 by roninsalsolo