Hey! Sorry for the delayed response. Been a busy week and I haven't been able to check the forum.
The first thing that jumps out at me is the second group of code. Unless your custom post type 'groupe' is assigned as a CPT-onomy to itself, the post type that you use for get_objects_in_term() should be different than the post type you use for the query posts $args.
It looks as if you mean for 'origins' to be in get_objects_in_term(). Try this:
$objects = $cpt_onomy->get_objects_in_term( $post->ID, 'origins' );
$args = array(
'post_type' => 'groupe',
'post__in' => $objects,
'orderby' => 'title',
'order' => 'ASC',
);
query_posts( $args );
if ( have_posts() ) :
?><ul><?php
while ( have_posts() ) : the_post();
?><li><a href="<?php the_permalink(); ?>" title="<?php the_title(); ?>"><?php the_title(); ?></a></li><?php
endwhile;
?></ul><?php
endif;
Let me know if this helped... or if you already figured it out =)