It isn't only the security. Your line $req = 'index' if -e $req; will make all requests invoke "index". Your code means " assign to 'index' if a file named $req exists". I am not sure what you wanted to achieve that way, but here is how I would do it.

use strict;
use warnings;

my $req = $ENV{QUERY_STRING};

# limits the applicability. Only lowercase file names
$req = lc $req;

# remove all unwanted characters from the beginning of the 
string. # In this example, everything except alphanumerics
# and underscore is removed.
$req =~ s/^[^a-z_0-9]+//;

# remove an extension, if any
$req =~ s/\.html$//;

# default value is the index
my $page = "pages/index.html";

# if the page exists, then we use it
$page = "pages/$req.html" if  -e "pages/$req.html" ;
[download]

Also, consider using CGI param instead of reading the environment.

HTH