The design of the European DEMO, i.e., the future fusion tokamak planned after ITER, is being developed under the coordination of the EUROfusion Consortium. This paper reports the design optimization of the toroidal field (TF) winding pack and its corresponding react-and-wind conductor, and a new design study of the central solenoid (CS). The optimization of the TF coil is driven by the results of the mechanical analysis that revealed an unacceptable stress accumulation in some locations of the previous proposal of the TF winding pack. The design study of the CS coil is done with the aim of minimizing the outer radius, while maintaining the magnetic flux defined in the PROCESS system code. The results of the design study, namely the optimized CS coil radius, current density, hoop stress, and the field map, define the initial information that will be needed in future for designing the DEMO CS winding pack and conductor. Contrary to the former similar studies, no upper limit is set for the peak field of the CS, implicitly allowing the use of high-temperature superconductors wherever the current density of Nb3Sn at the operating field is too low.