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How, for instance,  was the distance between t and u derived?

Dale, you are right: there would be no other method that triangulation and simple trigonometry.

From the drawn picture, we simply have to dig a bit deeper.

E.g. for point "u" :

(1) - It had to be some kind of "built up" point exactly South of "t", the latter being exactly south of its predecessor, ... and all the way to the Reference Point (probably point "r" here actually). And :

(2) - It also had to be visible from "Panthéon" as well as from Brie and Montlhéry, and visually checked as exactly aligned between these 2 latter points.

These simultaneous constraints must have been the hardest part of all to fullfill.

I suspect they had to use some 1st order corrections for small offset positions.

Thus the angular distance from Montlhéry to "u" could be measured then computed. Hence the distance from Brie to "u" was known.

Proceeding likewise for "t", and the " t, u, Brie " triangle could be solved. Hence the distance from "t" to "u" was known.

Und so weiter ...

Drawing on the picture all the "visual lines used" would have brought a lot of clutter. Only the "frame" has been published. It also ensured some confidentiality.

I see no other similar method. Who says simpler ?

Kermit