The factual answer in post #8 left off a bit.
As noted, the aprons are buffalo leather. What’s not mentioned is that each legionnaire had to procure his own apron off a live buffalo using just his axe. Only the survivors make it into the parade.
Just kidding. 
But someday this will be a widely believed urban legend and only us 'Dopers will know the true source of the oft-repeated & circularly-sourced story of the legionnaire’s axes.
In other military ceremonial weirdness - the Royal Welsh Regiment has appointed a new goat Fusilier Llywelyn.
This is my Axe!
This is my gun!
One is for chopping, one is for fun!
That’s nothing. The Norwegian Royal Guard’s penguin was knighted…
Aha! This clears up a detail about the Battle of Waterloo that I’ve always wondered about. There was a famous skirmish at Château d’Hougoumont:
The fight was recently dramatized in Jonathan Strange and Mr. Norrell.
So, why would Sous-Lieutenant Legros be wielding an axe in battle instead of a rifle and bayonet? Because he was a pionnier, and was tasked with breaking through fortifications such as the gate at Hougoumont!