Would 'intermediate bodies' work in English? Because we also have the phrase 'les organisations représentatives', but what is meant here is the idea that they are the middlemen in a way between the people and the rulers, which is not conveyed by 'representative bodies' as well.
I don't think intermediate bodies works; it certainly doesn't for me. But I think that I might have been a bit off target with my suggestion because I attended more to syndicats that to the other types of body.
I don't think there is a generally-agreed way of referring to such bodies (in Ireland and Britain, at any rate). I think that is partly because bodies like that tend to operate separately: the idea of la vie associative does not have the same resonance for us as it does in France. How would I refer collectively to bodies like the Chamber of Commerce, the Tidy Town Committee, the Twinning Committee, and their ilk? The best I can do is community associations, and I don't think that has the sanction of being a universally-adopted term.
"Civil society organizations" me semble pas mal pour exprimer le (1). On aimerait qu'il existe encore une société civile naturelle, dont les organisations ne soient pas complètement co-optées par le pouvoir central, même si ce n'est plus le cas.