DISCLAIMER: This method mostly works for those who uses/emulates Xbox 360 controller via DS4Windows, DSHidMini, XOutput, X360CE, etc so not sure if the developer will plan to add support for other controllers. This also could be a hit or miss so if it goes wrong, sorry I can't help. Pretty sure you'll need to install Style Switcher[www.nexusmods.com] as well but make sure to use the dinput8.dll from the Github link.
Edit: It also works without the Style Switcher mod/Vanilla.

Credits to muhopensores for the files.

- DMC3SE v1.3.0 Update[community.pcgamingwiki.com]
- DirectX Redistributable (June 2010)[www.techpowerup.com]
- Visual C++ Redistributable All in One[www.techpowerup.com].

So far tested on Xbox controller, Generic Gamepad, and PS4 controller.

• Download the Gamepad Fix[github.com] archive. OPTIONAL: If your controller does not support the current SDL2.dll, update the file by using the latest release of the x86 version of SDL2[github.com].
  
• Extract and place the downloaded files to your DMC3 directory.
  
• It is necessary to rename/delete the "dmc3se.ini" file to make the gamepad fix work.
  
• Run the game and see if the controls worked. You can display a menu by pressing Insert key.

• Run "install.bat".
  
• When prompted, enter "0".
  
• Extract and place the downloaded files to your DMC3 directory and replace "dinput8".
  
• It is necessary to rename/delete the "dmc3se.ini" file to make the gamepad fix work.
  
• Run the game and see if the controls worked.