The paper considers how a film of bismuth ferrite BiFeO3 (BFO) is formed on a polymeric flexible polyimide substrate at low temperature ALD (250 °C). Two samples of BFO/Polyimide with different thicknesses (42 nm, 77 nm) were studied. As the thickness increases, a crystalline BFO phase with magnetic and electrical properties inherent to a multiferroic is observed. An increase in the film thickness promotes clustering. The competition between the magnetic and electrical subsystems creates an anomalous behavior of the magnetization at a temperature of 200 K. This property is probably related to the multiferroic/polymer interface. This paper explores the prerequisites for the low-temperature growth of BFO films on organic materials as promising structural components for flexible and quantum electronics.