Solved

I’ve solved it by myself.

The WordPress function get_the_term_list() returns the terms of the post, but unfortunately they are in the reversed hierarchical order, so I had to turn them around.

$id = get_the_ID(); 
$terms = get_the_term_list( $id , $taxonomy , '' , $randomstring );

$terms_array = explode( $randomstring , $terms );
$terms_string = implode( $separator , (array_reverse($terms_array)));

$terms_string can nou easily be integrated into the breadcrumb.