Soufflet (m)
(with) definite article: lemechanical device used to supply the bag with air
Bellows, with an internal valve (➺ Soupape); NB¹: In bagpiping sometimes called "soufflet de bras" [arm bellows]; NB²: Common types are, according to their shape, the "soufflet rond" and "~ trapézoïdal"; NB³: In their catalogue, Pajot Jeune (à Jenzat) also mention a "soufflet demi rond", modèle Auvergnat, and even a "soufflet à plis", modèle Béchonnet [which in my perception is rather odd, because "pleats" are a common feature of all types]; NB4: In French, a manufacturer of bellows (in a general sense, i.e. for various uses) is called a souffletier.
According to Perre, "usually a cushion (pad) is attached to spare the arm of the piper".
Chassaing, Jean-François: La tradition de cornemuse en Basse-Auvergne et Sud-Bourbonnais [Thèse de doctorat, ethnologie 3e cycle, Univ. Lyon 2, 1981]. Moulins, 1983 (© 1982), p.12, 14.
Ricros, André (et al.): La cabrette: histoire & technique d'une cornemuse. s.l. [Riom], 2017, passim [23x (a.o. p.107 (~ de bras).
Ricros, André & Chavanon, Michel (Recherches en archives): Les facteurs de cabrette. In: Ricros (et al.): La cabrette… (2017), p.383 (catalogue Pajot), 393 (souffletier).
Ricros, André: Emprunts esthétiques, musicaux et lexicaux de la cabrette à la musette de Cour. In: Ricros (et al.): La cabrette… (2017), p.550 (~ à plis)).
Perre, Didier: Un des territoires de la cabrette, la Haute-Loire. In: Ricros (et al.): La cabrette… (2017), p.689 (➺ coussin [cushion]).