There's various things you can do.
You can rewrite it in C. Without actually seeing the code, I don't know how much trouble that would be. Much C++ code is simply C with a few addons, and some makes heavy use of templates and overloaded functions and such.
If you're not doing this, you need to make it communicate well with C. This means providing an interface for C, and surrounding it with extern "C"{ ... }
so the C++ compiler will know to make the interface C-compatible. Again, without knowing something of the C++ code, I can't tell how much work this would be. You'll need the wrapper for either of the following solutions.
You can make this a C++ project, surround every C file with extern"C" { ... }
, and just link it in. If you have any C++ files, the whole compilation has to be C++.
You can make a separate library to be linked in.
What you can't do is compile C and C++ together with a C main() function, or with a C compiler. C++ is more demanding, and requires more from the main() function.
You could always try recompiling the C files you're using as C++, and wrapping the .h files for the libraries in extern "C" { ... }
. Well-written C90 isn't that far from being legal C++ (although the C99 standard moved away from that some), and the compiler will flag any conversion problems you find.
Which of these is the best idea for you depends on questions like:
How easy is the C++ code to convert?
How easy is it to write a C wrapper for the C++ functionality you want?
How many changes are you willing to make to the C code?
How familiar are you with making a Linux library?