I've renamed that placeholder from <TMPL_VAR NAME="PERLCODE"> to <RECAPTCHA>.

Now it's not an HTML::Template placeholder so H::T won't know what it is.

use HTML::Template;
use Captcha::reCAPTCHA;

my $c    = Captcha::reCAPTCHA->new;
my $html = $c->get_html('your public key here');

my $t    = HTML::Template->new(scalarref => \$template_file);
$t->param(html => $html);    
$output  = $t->output;
[download]

Change your template placeholder to <TMPL_VAR NAME="html">.

Untested.

You can't put Perl code in a H::T template. That, imo, is A Good Thing. Keep all the code in your script and leave H::T to look after the presentation (the view).

It's worth having a good read of the docs. While you can't put code in the template there are some nifty things you can do that will make your life a lot easier.