The two-stage (TS) multibeam klystron (MBK) technology has recently attracted significant research attention due to its compactness and high-efficiency (HE) performance. However, there is still a lack of scientific research on the beam optics for such microwave power sources integrated with a postacceleration (PA) gap. In this article, a comprehensive optics study based on the newly developed 2-D optics code CGUN is conducted for the first time to demonstrate the most critical steps in the optics design process, by adopting the 400-MHz TS MBK for the future circular collider (FCC) as an example. Two specific challenges arise in this TS MBK, which are studied in this article, and solutions are given. First, due to the combination of slow electrons, impedance change from individual beamtubes into common volume, and the mild decay of the magnetic field, there are possible reflected electrons at the collector entrance. This requires an increase in the beam voltage to 80 kV, beyond the requirements from considering the output gap alone, as well as tighter control on bouncing electrons. The beam scalloping is also found to be highly sensitive to the position of the PA gap and magnetic field, which later demonstrates that large gap length and magnetic field are required. Final all-in-one particle-in-cell (PIC) simulations of this klystron equipped with this special optics design demonstrate that the specification of 1.2-MW continuous wave (CW) power is practically attainable with an efficiency of 77.5% and without the presence of reflected electrons at any point in the whole circuit.