No, actually I think that the Italian passato prossimo works pretty much like the French one (called "passé composé" in French). I think that to be simple, you can remember that for verbs describing a bodily motion (in the general case), you'd have to use "to be" instead of "to have" in italian :)
I suppose that makes sense but I thought "a tavola" meant more generally sitting down at the table, having a meal together, the setting of the food on the table, etc. So I translated the above as "He has just come to eat." Are these other meanings just colourful extensions of the idea of an "eating table"?
Yes, it does require "essere" :)
Passato prossimo is used as a kind of "past in present" form, so it's translated in English by the present perfect tense (which contains "present" in its name ;) ) If you wanted to say "He had just come to the table", I think you'd have to use the "trapassato prossimo" (instead of using the present form for the auxiliary, you have to use it's imperfect form (imperfetto) ), so it would be : "Lui era appena venuto a tavola" :) I hope I made myself clear ;)