Are ADUs allowed in Franklin, TN?

Yes, as an accessory use where the Section 5.2.6 table permits them. Franklin regulates accessory dwellings directly in Section 5.2.7.A: maximum one per lot; on a single-family residential lot the owner must be a permanent occupant of the premises; the building footprint may not exceed 50 percent of the principal building's footprint; an existing accessory structure may be converted if the conversion does not increase any dimensional nonconformity; parking is one space per unit under Section 10.2.3. Which districts allow accessory dwellings comes from the Section 5.2.6 table, so confirm your district's column with Planning before relying on an ADU design.