I have heard many times that C and Python/Ruby code can be integrated.  
Now, my question is, can I use, for example a Python/Ruby ORM from within C?
Yes, but the API would be unlikely to be very nice, especially because the point of an ORM is to return objects and C doesn't have objects, hence making access to the nice OOP API unwieldy.
Even in C++ is would be problematic as the objects would be Python/Ruby objects and the values Python/Ruby objects/values, and you would need to convert back and forth.
You would be better off using a nice database layer especially made for C.
Can I use a Python/Ruby ORM inside C?