In reply to mysterion:
Generally you'd walk on the windward side low enough down the slope to limit the risk of falling through the cornice ie at a level where you hope there is solid rock directly below you.
You'd not want to walk on the lea side as there might be the danger of the cornice falling on your head and the cornice may become a formidable obstacle if you need to regain the crest.
You might walk on the crest if there is no cornice as this allows a chance of jumping into Italy if your partner falls into France.