You have to rename the template file that you want WP to use as default.
The name is page.php. WP always uses page.php in case default template was specified in post editor.
If you have something like page-fullwidth.php which you intend to be
the default template rename it to page.php. Before – and only in case there is already a template named page.php – backup this file due to renaming, e.g. into page-default2.php. Later you could still choose page-default2 in post editor.
SO far, i am late to response to an 4 month old problem. May be it helps
someone else. Cheers,