Second, use File::Basename to get the basename (and don't forget your header!):

use strict;
use CGI qw(:standard);
use File::Basename;

my $file = param('file');
my $name = fileparse($file);

print header;
if (open (FILE, $name)) {
   my $data =  do {local $/; <FILE>; };
   print $data;
}
else {
   print "can't open '$name'";
}
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jeffa

L-LL-L--L-LL-L--L-LL-L--
-R--R-RR-R--R-RR-R--R-RR
B--B--B--B--B--B--B--B--
H---H---H---H---H---H---
(the triplet paradiddle with high-hat)