Thanks to both of you!
I won't have it in my hands before Christmas, so I don't have much more details to share here.
To me, it seems that the blade is triangular and hollow-ground on all faces, but I'll see that better when I get it.
Regarding the attribution, French or British, it will definitely need more research. Though the sword in the Royal Armouries collection is described as French, as well as this one :
https://www.pop.culture.gouv.fr/noti...45ab7cb1bca%22 . Maybe I should try to find Norman's book on smallswords?