This repository shows how to use websocket-sharp as a C# client, and websocketpp as a C++ server, all while (probably, not tested) staying cross-platform. This method allows you to effectively communicate between two different applications that both use different languages.
The C# side uses websocket-sharp, so you might need to install that (you can get it via nuget package manager). The C++ side relies on asio and websocketpp, both of which are included already so no need to install anything