Print views fields in a custom view page template
You are using template for display, here you will do theming for overall display, the $fields variable is not available here. 

If you want to change how fields are printed relative to each other, row style, then you should use views-view-fields.tpl.php, in your case the name will be like views-view-fields--yourpagename.tpl.php.

but if you want to theme individual fields then you have to use views-view-field--yourfieldname.tpl.php.