You are right, when "parents" or "documents" parameters aren’t initialized to any id, the filter parameter doesn’t work

This configuration is not tested on the ajaxSearch demo site because I always use the "parents" parameter to set to English or French documents. So I never noticed this issue.
Is somebody do the following test (I have done it but I would like an another independent test) ? Thanks for your feeback.
1°/ in the classes/search.class.inc.php around the line 1333, change the line
if (!strlen($this->listIDs)) return; // listIDs ='' means all documents
by
if (!strlen($this->listIDs) && !$this->cfg['filter']) return; //! listIDs ='' means all documents
and then
2°/ adds the template parameter in the displayed fields list. For that, always in the search.class.inc.php file around the line 568 replace the line
'displayed' => array('pagetitle','longtitle','description','alias','introtext','menutitle','content'),by
'displayed' => array('pagetitle','longtitle','description','alias','introtext','template','menutitle','content'),Thanks for your feedback about this fix.
Issue registered as
AJAXSEARCH-47