Joints and breaks give the first clues. A wooden moulding is fitted in lengths: you can make out joints between two strips or at the corners, sometimes nail heads under the paint. A run cornice usually continues in one piece, while staff is fixed in sections, glued or bedded in plaster. Where a piece has chipped, wood shows its fibres and plaster a whitish break, reinforced with tow if it is staff. Under thick layers of paint the two can look alike: in that case, have a professional examine an inconspicuous corner.
Consistency then tells you what is original. Identical profiles from one reception room to the next suggest a unified scheme; a profile that changes halfway along a wall points to a later repair, and a cornice cut off sharply by a partition betrays a room that has been reconfigured. The street-facing rooms, used for receiving guests, had the richest décor: a simpler vocabulary on the courtyard side is nothing to worry about.
For a damaged plaster cornice or ceiling rose, contact a fibrous plasterer, a plâtrier-staffeur in French, whose trade is making and restoring this kind of décor. Old woodwork that can be saved should go to a restorer, who will assess its condition before any work. When the wooden element has disappeared or can no longer be saved, the answer is a new piece made to match.