I understand that, on a digital camera, "exposure compensation" actually alters signal amplification, similar but not identical to changing the sensitivity.

In general, this is not how the term is used. Instead, "exposure compensation" means: tell the camera's exposure program in automatic exposure modes to target an exposure brighter or darker than the meter reading. (More at What is exposure compensation?, and at How do DSLRs figure out what aperture to select in P mode?)

One way the program may respond to this is by altering the amplification, increasing the effective ISO. (More at How is ISO implemented in digital cameras?) It can also change the shutter speed or aperture — but that will depend on the mode.

On a film camera, changing the amplification is not an option, so to change the exposure, shutter speed or aperture must change. However, you might not perceive them changing, because the camera doesn't actually stop down until the shutter clicks, and it's hard to hear the difference between, say, ¹⁄60th vs ¹⁄₁₂₅th of a second.

Nikon actually includes the "program chart" for the F6 in the manual:

… so you can see exactly what it does. For example, if the meter returns "EV 5", you'd get an aperture of f/4 and a shutter speed of ¹⁄₆₀th. And, you can see that it's really quite a simple algorithm. As noted in this answer, some cameras let you select between different programs. On some entry level cameras, a setting like "sports mode" actually means "select a program which prioritizes high shutter speeds" — even if there's no direct, named control over the program. Generally, though, if you really care a lot about a particular exposure factor, you would use Aperture or Shutter Priority.