It's not immediately clear from the docs, but just saying use IO::Handle entitles you to call IO::Handle methods on normal file handles like your already opened $fh.  In other words, your snippet could be simplified as follows:

use IO::Handle;
open (my $fh, '<', $FILE) or die $!;

# then simply call method from IO::Handle
$fh->getline();
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This doesn't answer the question how to make a socket out of a regular file, but I thought it's worth mentioning nevertheless...