It's a bit difficult, because a FILE* can read/write from a file handle which isn't associated with a named file at all (for example an unnamed pipe or a socket). You can obtain the file handle with fileno() and then there are system specific ways to learn about the file name. Here's a discussion on how to do this under Linux:
Getting Filename from file descriptor in C
and under Windows this isn't much easier either:
http://msdn.microsoft.com/en-us/library/aa366789(VS.85).aspx (as an extra step here, you use _get_osfhandle() to get the Windows file handle from the c-library file descriptor)
