Pressure-assisted melt filling (PAMF) of pre-fabricated micro-capillaries has been proven an effective way of fabricating hybrid optical fiber (HOF) from unusual combinations of materials. Here, we extend the applicability of PAMF to multi-anionic fluoride-sulfophosphate (FPS) glasses. FPS glasses provide extended transmission windows and high solubility for various transition metal (TM) and rare earth (RE) ion species. Using PAMF for fabricating FPS/silica HOFs can therefore act as a platform for a broad variety of optically active fiber devices. For the present demonstration purposes, we selected Cr3+- and Mn2+-doped FPS. For both glasses, we demonstrate how the spectral characteristics of the bulk material persist also in the HOF. Using a double-core fiber structure in which waveguiding is conducted in a primary GeO2-SiO2 core, mode coupling to the secondary FPS-filled core allows one to exploit the optical activity of the doped FPS glass even when the intrinsic optical loss is high.