That’s the pioneer detachment of the Legion.
Traditionally, these soldiers performed certain combat engineer functions, like clearing obstacles from in front of the marching column. Hence the traditional axes.
Being a pioneer was considered a fairly prestigious assignment for experienced troops. And as part of their esprit de corps, beards were mandatory.
I’m just going off the top of my head here, so if anyone has more detailed information on the Legion, by all means correct me.
I was basing my opinion on a expose done on Americans serving in French Foreign Legion many years ago.
The pioneers are the leading unit of marchers in parades on Bastille Day. There are French citizens in the Legion, but they are signed up as citizens of other countries. After honorable service Legionnaires are given French citizenship. Their officers are always French.