Interfacing with non-C API libraries
The way that an FFI interface is built and and used shouldn't change too much with the language used to build the library. Most reasonable libraries offer a C API, which will then be largely equivalent no matter the language actually used in the library.
If a library does not offer a proper C API, however, then all bets are off. This is normally the point where any reasonable developer will give up and write a custom C API adaptor library to interface through. That is not strictly necessary, at least not all the time.
The calling convention of any dynamic library is still at its core a C calling convention [citation needed, the author does not know if this is true but thinks it is]. So, if one is sufficiently persistent and industrious, it is possible to write an FFI interface to libraries that do not offer a C API.
Interfacing with C++ libraries
Perhaps the most common non-C API used by libraries is the C++ API. For example, the Clang Tools Organization provides the LibTooling C++ library as an alternative to the C API libclang library. Often a C++ API may be more powerful or convenient than a pure C API. Thus, it is a tempting idea to interface directly with a C++ API.
There are quite a few issues to deal with when writing an FFI interface to a C++ library. Some of these may not be solveable, while others may actually work in your favour. Let's explore some of them: