You got me on that one!!
As you stated the actual French polishing process was perfected and developed by the French in the early 1800's but shellac was being used as a common finish in the 1700's in England and for several hundred years before that in Asian countries. I believe that I read somewhere that they found a piece in an Egyptian tomb that was finished in shellac.
living in France makes things easier regarding this
shellac or bee's wax, but some varnish were also developed in
the XVIII to mimic chinese/japanese lacquer.
In the time that the desk was made they would have been simply applying shellac with a brush or pad but most likely not doing the full polishing process if that is the finish on it.
I really like to apply finish with a pad, be it varnish or wax.
It gives you a good way to have a nice thin finish and no brush marks.
Here in the states we give people a had time and tell them that they're not French polishing. They're just putting shellac on with a rag if they don't really know what they're doing.