Découpe olivette

09:38 Dec 23, 2018 

Think you`re probably correct. Settled for underarm as out of sight in this context.
Have a very Merry Christmas and Happy New Year.

17:26 Dec 22, 2018 

Since following this wuestion, I saw what I think was exactly this just the other day!
It was a straight piece of fabric (sleeve, I think?) with a slit in it, and behind the slit was sewn an oval (a bit pointed really, more like a almond) in what happened to be a contrasting colour; so when flexed, the slit opened and the additional fabric became visible; I feel sure this is what was being described here.

17:12 Dec 15, 2018 

As firefighters' clothing needs to give protection against fire, water, chemicals and other nasties, I suspect that they really don't want armpit vents.

16:39 Dec 15, 2018 

I suspect that may be a red herring: I've a feeling that the button-and-loop fastening might just be incidental — something that is used to close a gusset when not needed; very much as you also have the tab-and-velcro fastening to close the 'soufflet' gusset at the cuff.

14:14 Dec 15, 2018 

Discovered that an "Olivette" is a button and loop fastening, perhaps covering your oval shaped inset. Let`s see what else turns up.

14:09 Dec 15, 2018 

I've a feeling I've seen something like this, with a sort of inset oval-shaped piece of fabric to replace the underarm seam, presumably to give a little more movement at that point that otherwise has a tendency to "pull" — could it be that, d'you think?