Success. Here is how to retreave a cookie:

my $cookies = Apache::Cookie->fetch();
my ($name, $value);

# 'license_session' is the name of the cookie 
# I am looking for.
if ($cookies->{license_session}) {
    $name =  $cookies->{license_session}->name();
    $value =  $cookies->{license_session}->value();
}

print "<h3>name = $name</h3>\n";
print "<h3>value = $value</h3>\n";
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