Hello! Do you have any special reason to use C# for your game? If not, maybe you got to do something else.
You need a game engine. Unreal Engine 4 is a good one and have a tutorial on how to build on Linux ( https://wiki.unrealengine.com/Linux_Support ). In this case, the guide is specific to Ubuntu, but you can do the proper passwords on your Fedora.
If you don't want anything complex, you could use PyGame ( http://pygame.org/ ) which I think is very easy to use and there's a lot of documentation to learn about it.
In case you still want to use C#, you will have to use MonoDevelop ( http://www.monodevelop.com ) or Eclipse with Emonic ( http://emonic.sourceforge.net/index.html ). Both of them on Fedora repositories.
Best regards!