If you create page-home.php you should see your changes, but check @Foxaii’s post because this may not be the structure you want.
In your structure, everything will work nicely if your page title is “Home”, but if that gets changed then Roots will no longer use the template you created. If you always want your Front Page to use a particular template, regardless of its title, ID, or slug, then consider using the front-page.php and base-font-page.php structure suggested by @Foxaii.
For more reading and a great basic explanation you might also check out this post: Development using Roots