Actually with a few small modifications your starter code as shown in the OP is able to do what you expected from it (showing you the file names):

#!/usr/bin/perl

$/ = '';   # read input by paragraphs

@file = <>;

for($i = 1; $i < @file; $i+=4)  # from field 1 (2nd field); and += for
+ proper loop
{

    print "$file[$i]";
}
[download]

Edit: Oops, it's $/ = '';  # not undef