Throwing C++ exception through C function call

This is platform-specific and compiler-specific question.

For example, on Linux/GCC, you have to compile C code with -fexceptions option, then unwind tables would be build and exception will go throw C code.

From https://gcc.gnu.org/onlinedocs/gcc-7.3.0/gcc/Code-Gen-Options.html#index-fexceptions

-fexceptions

Enable exception handling. Generates extra code needed to propagate exceptions. For some targets, this implies GCC generates frame unwind information for all functions, which can produce significant data size overhead, although it does not affect execution. If you do not specify this option, GCC enables it by default for languages like C++ that normally require exception handling, and disables it for languages like C that do not normally require it. However, you may need to enable this option when compiling C code that needs to interoperate properly with exception handlers written in C++. You may also wish to disable this option if you are compiling older C++ programs that don’t use exception handling.

I'm less familiar with Visual C++/Windows development, but I believe exceptions handling will use common mechanisms if you compile your C++ and C code with /EHa option (allow mix of structured and C++ exceptions)