A little perplexed

A few days ago, during a raid on eBay, I was able to secure some interesting miniatures, at a very cheap price. They are old Minifigs Revolutionary French, and I looked at this as an affordable way to beef up my French Revolutionary Army in the hope, sooner rather than later, to get into Valmy, or Suvorov's Northern Italian campaign.
The package was delivered today. It included cuirassiers in bicorne and grenadiers in bearskin, who were exactly what i expected. In the lot, nevertheless, there were also two blisters of "Line Fusiliers or Light Chasseurs, leather caps." I confess I was not really sure what to expect; in my naivete, I was thinking something closer to a Phrygian hat. Well, I was wrong. What these figures are wearing is a type of cap, almost a casquet or helmet, I have never seen before. I went online, and I googled, until I finally found a reference from Napoleon's expedition in Egypt. Here's the related picture:

I am talking about the hat shown on the two figures at the center. What exactly is this? And what do I do with these miniatures? My first reaction was to "dilute" their presence mixing them with traditional infantry in bicorne. Or Tarleton. That would look more revolutionary to me. Could they stand in for Valmy infantry? Plus, does anyone produces 15mm infantry in Phrygian cap? That would be cool.
I am still scratching my head on this development. Not sure where this development will bring me. Need to think about.