You haven't told us much about your network. Like how you access these files outside of Perl.
If this is all a local, behind-the-firewall network, you should look at
NFS. Then your filesystem can be distributed over several machines, but appear to be a single filesystem on the working machine.
If that's not an option, your best bet (for simplicity) is to set up a web server on the remote machine and access files in Perl using
LWP.