"Could" seems to talk about ability:
I could take all of next week off from work. (I have enough vacation days left).
Here, I have the ability to take the next week off. There is no suggestion that I think that I want to, or that I intend to. Perhaps I'm merely laying out my options, before I decide if I want to do it or not.
In contrast, "might" seems to talk about possibility:
It might rain tomorrow
and if the subject is human, it talks of intention:
I might take all of next week off from work.
Here, I'm not just saying that I'm able to take the next week off, but that I have some intention of actually doing it (but that I'm not 100% sure that I actually want to or not).
But in French, according to this website, both "could" and "might" are translated by using the verb "pouvoir".
1. Is this distinction between "could" and "might" possible to communicate, in French?