There is currently much interest in materials and structures that provide coupled ferroelectric and ferromagnetic responses, with a long-term goal of developing new memories and spintronic logic elements. Within the field there is a focus on composites coupled by magnetostrictive and piezoelectric strain transmitted across ferromagnetic-ferroelectric interfaces, but substrate clamping limits the response in the supported multilayer configuration favoured for devices. This constraint is avoided in a ferroelectric-ferromagnetic bilayer in which the magnetic response is modulated by the electric field of the poled ferroelectric. Here, we report the realization of such a device using a diluted magnetic semiconductor (DMS) channel and a polymer ferroelectric gate. Polarization reversal of the gate by a single voltage pulse results in a persistent modulation of the Curie temperature as large as 5%. The device demonstrates direct and quantitatively understood electric-fieldmediated coupling in a multiferroic bilayer and may provide new routes to nanostructured DMS materials and devices via ferroelectric domain nanopatterning. The successful implementation of a polymer-ferroelectric gate fieldeffect transistor (FeFET) with a DMS channel adds a new functionality to semiconductor spintronics and may be of importance for future low-voltage spintronics devices and memory structures.