Before the_content is displayed WP looks for filters to run the content through. One of those filters is do_shortcode. The idea of a filter is that you can change something before it is displayed. As a consequence, if inside the filter function you echo something, it ends up before the_content, which is still waiting for the filtering process to be completed.
Since your function form_shortcode() does not return a modified content anything that is displayed must be the result of echo statements in form.php.