The /proc/pid/fd directory in Linux based systems contains the open files for that pid. The files are represented by the file descriptor number that the file has in that process. The files are links to the actual files that are open with that fd number in that process.

So just reading the /prod/pid/fd directory should be enough. You can then stat each of the files to find where the link is pointing. You should, however, consider the fact that you would require root access to do this, as the fd directory is readable only by the user who owns the process.