“He” is related to a person itself. In french, we also use it to talk about an animal or anything which is alive. I know you guys in english much often use “it” to define an animal with the exception for pets… sometimes.

And “it” is related to something, an object, something which is not alive.

In the example you gave, it will then be “He” because we know you are talking about someone and not an object.

There is actually a distinction whether you want to imply the man will be sad or that the resulting situation would be a sad one

Could you contact him, otherwise he will be sad

Could be translated as you stated :

Pourriez-vous le contacter, autrement il sera triste.

Or, the one I prefer using “sinon” (a conjunction) instead of “autrement” (an adverb):

Pourriez-vous le contacter, sinon il sera triste.

On the other side, assuming this is correct English,

Could you contact him, otherwise it will be sad

Could be translated to:

Pourriez-vous le contacter, sinon cela sera triste.

Edit: as suggested by SG “cela” could be replaced by “ce” or even “ça” for lesser and lesser formality.

I find that one using that form less elegant though, but the more elegant way I think of is to complicated for me to explain. I give it anyway but I can’t provide much more grammatical insight about it :

Il serait dommage que vous ne le contactiez pas.

Which I would translate to:

It would be sad that you don’t contact him.

Hope this helps, sorry I can’t be more “technical” about the whole stuff