Fair Furniture Trade Act of 1985 - Amends the Trade Act of 1974 to authorize the President to enter into a trade agreement with Canada which provides for changes in the Canadian tariff treatment for U.S. furniture products. Requires such agreement to provide for the elimination of: (1) differing tariff levels on furniture trade between the United States and Canada; and (2) any Canadian nontariff barrier to U.S. furniture products. Sets forth factors the President shall consider in negotiating such agreement. Provides for staged increases in the tariff on imports of Canadian furniture until such a trade agreement is implemented. Directs the President to consult with specified congressional and other committees in negotiating such agreement. Directs the President to proclaim the necessary changes in the Tariff Schedules of the United States in order to implement such a trade agreement.