hook_query_alter, AJAX, views_get_view : have to submit twice
It was some kind of mess with the $_SESSION variable, which I used for independant reasons.

I corrected my code this way :

  if ($view-&gt;name == 'rechercher') {
    $view-&gt;query-&gt;add_table('field_data_field_cp');    

// Old code
// $view-&gt;query-&gt;add_where(1, 'field_data_field_cp.field_cp_value', '%' . 
// $_SESSION['filtres']['field_commune_value'] . '%', 'LIKE');

// New code
    $view-&gt;query-&gt;add_where(1, 'field_data_field_cp.field_cp_value', '%' . $view-&gt;exposed_data['field_commune_value'] . '%', 'LIKE');    
  } 


... and everything seems to be fine, AJAX and all. 

Thanks to Clive for the help.