The way I was taught this in French school is that the diaeresis causes the letter to be pronounced separately, so in maïs the "¨" forces you to say "a" and "i" separately (ah- ee) instead of together ("eh" as in "mais" which is an existing French word).
It only affects the diphthong AFAIK, so I agree with you that it's not the reason for why the "s" is pronounced out loud.
The final "s" is usually silent in French and I'm not aware of any rule for what defines the exceptions.
The outcome for the final "-s" is somewhat influenced by the origin of the word, as you would pronounce "bis" differently depending on whether you mean "beige" or half-whole-wheat bread, vs. if you mean "repeated" (from latin).
There are a bunch of such weird exceptions, like "vis" (screw, or past tense of "to see") or "bus" (bus, or drank) which both can be pronounced either depending on their meaning, or "os" which is different depending on plural vs. singular.
For the ending "-s" there is also some regional variation. Where I was born, you would normally pronounce the final "s" in words like "plus" or "moins", and I was very surprised as a teenager to meet people from other French regions who made fun of it.
> The final "s" is usually silent in French and I'm not aware of any rule for what defines the exceptions.
I don't think there is a rule. The 19th-century book said this:
>> L's s'est maintenu ou définitivement rétabli depuis plus ou moins longtemps dans maïs, jadis, fi(l)s et lis (y compris fleur de lis le plus souvent, malgré l'Académie); dans metis, cassis, vis (substantif) et tournevis. La prononciation de ces mots sans s est tout à fait surannée; on ne peut plus la conserver que pour les nécessités de la rime, et encore!
The reference to /s/ being maintained or reestablished, and the pronunciation without /s/ being out of date, suggests to me that the rule was that final /s/ was lost (in Parisian French, I guess...), and that there was a specific effort to put it back into some words. But that's speculation on my part.
It seems clear that bus "bus" and maïs "maize" have a final /s/ because they are foreign words. It's less clear to me why they're given those spellings as opposed to something more like busse.
It only affects the diphthong AFAIK, so I agree with you that it's not the reason for why the "s" is pronounced out loud.
The final "s" is usually silent in French and I'm not aware of any rule for what defines the exceptions.
The outcome for the final "-s" is somewhat influenced by the origin of the word, as you would pronounce "bis" differently depending on whether you mean "beige" or half-whole-wheat bread, vs. if you mean "repeated" (from latin).
There are a bunch of such weird exceptions, like "vis" (screw, or past tense of "to see") or "bus" (bus, or drank) which both can be pronounced either depending on their meaning, or "os" which is different depending on plural vs. singular.
For the ending "-s" there is also some regional variation. Where I was born, you would normally pronounce the final "s" in words like "plus" or "moins", and I was very surprised as a teenager to meet people from other French regions who made fun of it.