Actually film is technically both an analogue and a digital medium. Spatially film is difficult, since it is by nature digital, with an undefined sampling rate. Well for monochrome films it is, colour film is even harder to characterise, since you have to take into consideration the dye couplers, and I've not looked at that closely enough. With the monochrome films though you have the silver halide crystals distributed in the gelatin emulsion layer. Each crystal acts just like a digital sensel, in that it reacts to the total level of light incident upon it. If the emulsion layer was only a single crystal thick, the crystals were all of an exactly uniform size, and they were evenly distributed within the emulsion, the it would be truly spatially digital, just like our electronic sensors. Some high speed films may even have large enough silver halide crystals that they start to approach this situation more closely. The slower "fine grain" films will have much smaller silver halide crystals that will be distributed in depth within the emulsion layer, as well as in the horizontal and vertical axes. Because of this three dimensional distribution the spatial sampling rate becomes far more complex.
Although the physical interactions of the photon is very similar in just about all sensor systems, chemical films, or electronic sensors of various types, it is the processes that happen after exposure that vary widely. Film uses a chemical process to convert the record of the number of photons arriving at any sensing unit, AKA as the silver halide crystal, and this process can result in the crystal having an infinitely variable level of optical density. By definition this is Analogue information, since it is not limited to a restricted set of integer values. remember that you can record more than just two dimensional images using optical films. For example the audio track in many cine formats is actually recorded as a signal of varying optical density, and is also still an analogue signal, just as it would be if recorded on say, 1/4" tape. Don't forget either that the brightness signal from many electronic optical sensors has been recorded directly to a magnetic storage medium, as a truly analogue signal. Oddly enough though you could actually use film as a storage medium for digital signals, which could even include what we consider to be purely digital images, both spatially and for brightness.