You cannot do that because some languages implementations could have an ABI different and incompatible with the C one.
On current systems, C is very common and most (but not all) language implementations have an ABI and calling conventions compatible with the one from C. Notice that it is a property of the implementation (your C compiler and your operating system), not of the programming language.
If using C++, beware of name mangling and of exception handling. (e.g. C longjmp is not friendly with C++ exceptions). Dynamic loading facilities like dlopen and dlsym are relevant to name mangling. So prefer an API using extern "C" functions.
Memory management (notably with garbage collection) is also an issue.