Because this game was made by Ubisoft, there is a possibility that there is more than one crash-on-startup bug. Follow these steps to determine if this is the bug you have.

The following error message will appear only when you attempt to start the game by double-clicking on the executable file. It will not appear when opening the game through Steam or Uplay.

To find the executable file:

1. Go to your steam library, right click on Rayman Legends, and click the properties button.
   
2. Go to the "Local Files" tab and click "Browse Local Files..."
   
3. Double-click on "Rayman Legends.exe".

If the following error appears:
then this guide is for you.

The fix is simple.

1. Enter the "_CommonRedist" folder, which should be inside the game files.
   
2. Enter the "vcredist" folder, and all folders after that.
   
3. There will be two .exe files in this folder, "vcredist_x64.exe" and "vcredist_x86.exe".
   
4. Open the file named "vcredist_x86.exe".
   
5. Choose the repair option, and press Next.

The game should now open.

If, for any reason, this guide does not help you, I wish you the best of luck. Consider requesting a refund from Steam Support or contacting Ubisoft support.