You need to think of the light as a superposition of frequencies. Entanglement is not important for this kind of thing, so the easiest way is to think of photon by photon propagation: each photon propagates following Maxwell's equations from a point on the incandescent filiament to the reflector to the photodetector. Now the photon can be thought of either as monochromatic, or as a quantum superposition of frequencies, as described in my answer to "How can we interpret polarization and frequency when we are dealing with one single photon?". Either way, you're simply resolving into Fourier components, and depending on what calculations you want to do, either method will often give the same results (see below).
So, in short, you need to talk of a separate Fresnel zone for each frequency. For many light sources, and setups the Fresnel zone positions are not greatly sensitive to wavelength if, for example, you want to think about the narrow, visible light band. So if your reflector took up only the central Fresnel zone, this is often roughly the same size as the Fresnel zone for all the frequency components. The error becomes more obvious for the higher order zones. Thus, for example, if you look obliquely at a coverslip, you can the Fizeau fringe pattern: the central region is white, but the higher order fringes are coloured.
What you might do with this now "ensemble" of Fresnel zones depends on what you want to calculate. The Fresnel zone idea is not so useful to my knowledge in polychromatic situations. So, for example, if you want to find the intensity pattern on the photodetector surface to understand what the photodetector sees, you simply work out the intensity pattern for each monochromatic frequency component and sum them all up (Parseval's theorem). You might want to put a frequency response into this intensity calculation to model the photodetector's response curves. You'll probably also want to sum intensity contributions over the different points of origin on the lightbulb filiament. Note that the result will be the same here if you think of photons arriving as quantum superpositions of colours (likely to be the more physical assumption), or if each of the field's colour components are carried by separate photons in the appropriate proportions: all the colour components are summed incoherently (intensity summed).