As I understand it, these seating arrangements were why we now describe the political spectrum in terms of right and left. So, in the trope-naming assembly, would a monarchist representative of the third estate have sat to the right or the left of a democratic-minded aristocrat?
The left/right divides in the French National assembly is really getting clear only in 1791, and is a political division.
On the left, the republicans includes Philippe Egalité (a.k.a. Louis-Philippe, Duke of Orleans), whose son will become King Louis-Philippe between 1830 and 1848, and heir of the crown after the son and brothers of Louis XVI ; and many franciscans priests. On the right, the Girondins, mostly republicans but with monarchists among them (at least till 1792).
So, to answer your question: a lowborn monarchist or parliamentarist would have been seated on the right, a noble radical republican on the left.
When the Estates general was meeting as a whole, for example during the opening ceremony, they were separated by estate and sat sort of like a horse shoe. Or rather, they were seated with the estate they had been chosen to represent. There were nobles and priests who had been elected by commoners, and they always sat with the third.
However, the estates were only in session in different rooms. In t was only after that, as has already been said, that the assembly was divided into left-right.