You need to load the C# from C++. Here is an article of the
Dynamic Loading.
The internal problem is, that Java, C++ and C# have own runtime environments, so you need in the project 3 runtimes which must interact. I guess it will be slow and crappy.
BTW: I would recommand NOT using C# from JNI, but wrapping all in C++. Alternativly: think about moving the C# logic to Java,