How to use TOC with ACF?

You can use the the acf/save_post action to copy the content from your
custom ‘full_text’ field over to the normal post content field, so it can automatically be accessed by toc+ and other plugins.

add_action( 'acf/save_post', 'wpse199256', 20 );

function wpse199256( $post_ID ) {
    global $wpdb;
    $post = get_post( $post_ID );
    $wpdb->update( $wpdb->posts, array( 'post_content' => get_field( 'full_text', $post_ID ), array( 'ID' => $post_id ) );
}

Depending on how you use your CPT this will lead to some templates etc. having to be adapted, if they were outputting the content field (which was empty until now).