Isn't that just tetracameral then?
Depends on whether they vote as separate bodies. "Cohort" might be a better word than "house," though, for each contingent.
I'm less familiar with the French revolution than I ought to be - so corrections are welcome, if done gently - but I believe one of the early victories by the...uh, common people (hate to use that expression, but it fits the time) was the decision that nobility, clergy and "third estate" representatives to the Estates-General would be rolled into one big body rather than treated as three separate ones. Thus the third estate could control the whole thing (because any decisions could be made by this one body in which they were numerically dominant, rather than having to pass all three).
A modern example: the Senate in Belgium consists - at least as it's laid out in the constitution* - of 40 members elected by the public, another 21 delegated by the parliaments of the (Flemish, French and German) "communities," and another 10, the so-called co-opted Senators, designated by the other two classes once they're in place
*(I add that qualification "as it's laid out in the constitution" because I learned in following the 2007 Belgian election that the question of how many seats go to each party, for all three classes of Senators, is determined by the popular vote, in a proportional-representation system; this three-cohort system applies to determining which individuals within party X get its seats). So you've got three different classes of Senators, in the sense that there are three different ways of getting there, but it functions and votes as a single house.
Perhaps DuQuense has something like that in mind.