I’ve never used FAU (Forced Air Unit) acronym, it was always furnace room or utility room
. Back to your question; it depends what type of a furnace you are going to install. For example, there are furnaces with adjustable / leveling bolts at its base that provide clearance above any type of flooring material.
Based on 5 furnace manuals that I have (2 from high efficiency furnaces; upflow and downflow. 90% AFUE and 3 regular 80% AFUE) a furnace cannot be installed directly on carpeting, tile (vinyl / linoleum, etc.), or other combustible material other than wood flooring.
In such cases the combustible flooring material should be removed / trimmed away from the base of the furnace to comply with the minimum clearance from combustible materials requirements provided by the manufacturer. Those vary between the manufacturers, furnace types, and locations, so you’d have to obtain the installation manual for your particular model.
Some manufacturers may allow a subbase for a downflow furnace installations
directly on a combustible floor (drawing below is from an American Standard upflow / downflow / horizontal gas-fired, direct vent condensing furnaces installation manual).
If installing a cased coil beneath the downflow furnace (vertical installation), a subbase is not required.
Let me know if this answers your question.