In the strictest sense, the Ancien Régime is the class system that existed within France before the French Revolution. More broadly, it may refer to any similar feudal or absolute monarchist class structure overthrown by bourgeois liberal reform or revolution.
The first estate refers to the clergy.
The second estate refers to the nobility.
It is common to describe some group that falls outside of typical political-economic structure as a "fourth estate." Most commonly this is understood to be the press, who are expected to be independent from class interests.