If I understand your question which is to be honest a little vague, you should be able to change if ( is_home() ) to if ( is_front_page() ) This will display the 'featured-content' template part on a static front page (i.e a home page) instead of the blog page. In Wordpress is_home = blog home page and is_front_page = static front page. A little confusing, but if you think WordPress was originally made for blogging, it makes perfect sense. is_home explained here is_front_page explained here
EDIT: If you want the featured grid to display everywhere, you should be able to remove the if statement so it just reads get_template_part( 'featured-content' ); that's assuming I have understood you correctly, and based on the limited code you have supplied. Hope this helps anyway.