The truth hidden in this anecdote and that is that it is literal- the wooden grip of the bisaiguë is lost, only to be found hanging on the kreuzaxt! And so the apprentice out in Normandy would search long and hard until making his way into the Jura of Alsace, (you see where the Compagnonnage/ Wandelgezell/ Journeyman,comes into the picture) where the street names are still in German and German and French identity is vague and the bisaiguë is still an axe.
Greetings,
Don Wagstaff