This paper presents a corpus study that investigates the question of word order variations (WOV) in spontaneous spoken French and its consequences on the parsing techniques that are used in Natural Language Processing. We have studied four taskoriented spoken dialogue corpora which concern different application tasks (air transport or tourism information, switchboard calls). Two corpora concern phone conversations while the other two correspond to direct interaction. Every word order variation has been manually annotated by 3 experts, following a cross-validation procedure. Our results show that, while conversational spoken French should be highly affected by WOVs, it should also still be considered as a rigid order language: WOVs follow some impressive structural regularity and they result very rarely in discontinuous syntactic structures. As a result, non-projective parsers remain well adapted to conversational spoken French.