Turn it on in the Catalog ... Product Types ... and click the EDIT LAYOUT button:
Product Free Shipping Image Status - Catalog
Show the Free Shipping image/text in the catalog?
Usually, you can use just the switch for this, but you want it to work one way on the listing and another on the product _info so the switch will not help you ...

Using your templates and overrides, you can customize the:
/includes/modules/product_listing.php

and change the line:
Code:
$lc_text .= '<br />' . (zen_get_show_product_switch($listing->fields['products_id'], 'ALWAYS_FREE_SHIPPING_IMAGE_SWITCH') ? (zen_get_product_is_always_free_shipping($listing->fields['products_id']) ? TEXT_PRODUCT_FREE_SHIPPING_ICON . '<br />' : '') : '');
so that you do not see it in the Product Listing ...