It seems like democracy is a form of government where there is a balance of power between citizens and the government. Would Foucault be in support of this type of government?
Foucault's own thoughts for or against things that he writes about, are often difficult to unravel. His first goal in writing is to allow us as readers to see something clearly which at first is not particularly clear. For example with the recent publication of his lectures, particularly, "Society Must be Defended", "Security, Territory, Population", "The Government of Self and Others" and "On the Government of the Living" one sees with great detail his concerns with the material developments and evolutions in the exercise of and contest of power, not just at the level of the State, but as diffused throughout our societies. Where his opinions really come to fore are in interviews, especially when being pressed for his perspective. So there's an answer to your question, but I wouldn't advocate looking for it in his books.
Insofar as power is never one-sided in his perspective, it applies to the dominated as much as to a dominator. In each field of genealogy or archeology of statements and events that he goes into, there's never much of an reason to say "yes this was good" "that was bad". That type of evaluation becomes irrelevant to his overall objective of letting you know the origins of where you are today.
So he engages, Plato, Artistotle, Cicero, Polibyus etc on their views on democracy, republic compromises etc, but it is to explore both the context of the relations of power in their epochs but also the types of knowledge they developed to deal with those concrete situations. So with everything he approached, there are situations, and how subjects deal with those situations. Its a massive project for the articulation of spaces of freedom.
So would he advocate democracy? He would ask what one means by that term. As he himself states in an interview, "you can’t provide a definitive formula for the optimal exercise of power." Part of his perspective is that it's not a question simply for him to decide. Power-relations are negotiated in the moment, in society, BY society, not just any singular individual, and always in our every-day present. What is, or what becomes, are the results of "relations of force" a la Nietzsche.
It's a somewhat vague response that never satisfied many of his peers and critics while he was alive. But it's something he doesn't veer from. He sees a great danger in trying to prescribe for the world particular a priori formuli and spent the entirety of his philosophical career fighting against such a priori's. His ultimate goal is freedom:
In an interview from Nov. 1980:
We have to rise up against all forms of power—but not just power in the narrow sense of the word, referring to the power of a government or of one social group over another: these are only a few particular instances of power.
Power is anything that tends to render immobile and untouchable those things that are offered to us as real, as true, as good.
What form that freedom takes is a matter of what we're capable of, not any preconceived notions. Maybe it's somewhat ironic, but Foucault was a philosopher that spends his career digging through the past, but was not in the slighted bit interested in living in it.