Fauteuil n. : An armchair; hence (because the members sit in fauteuils or armchairs), membership in the French Academy.

Fauteuil n. : Chair of a presiding officer.

Example:
What are brewster, spoonback and Fauteuil all types of?

Taxonomy
Fauteuil, free encyclopedia, gilded, arm chair, search, beech, gesso, reproduction, silk jacquard, Tassinari, Chatel, in the Blue Room, the White House, wooden frame, eighteenth century, made of wood, relief, seat back.

Defination from the web:
Fauteuil by Pierre-Antoine Bellange, c. 1815. Gilded beech, gesso, with 1996 reproduction silk jacquard based upon an 1815 Tassinari et Chatel document. ... A fauteuil is a style of open-arm chair with a primarily exposed wooden frame originating in France in the early eighteenth century. ...