This is the passage in Singh where he introduces the idea:
A century and a half after Kircher, in the summer of 1798, the antiquities of ancient Egypt fell under renewed scrutiny when Napoleon Bonaparte despatched a team of historians, scientists and draughtsmen to follow in the wake of his invading army. These academics, or ‘Pekinese dogs’ as the soldiers called them, did a remarkable job of mapping, drawing, transcribing, measuring and recording everything they witnessed.
Simon Singh (1999). The Code Book, p. 205. New York: Doubleday.
So if we are to believe Singh, “Pekinese dogs” was a nickname that soldiers in the French army bestowed on the academics. Where did Singh get this from? Unfortunately, Singh does not give citations for his claims, only lists of “further reading”, and for chapter 5, the only item of “further reading” that looks as if it might be a plausible source for Napoléon’s expedition to Egypt is W. V. Davies (1997), Reading the Past: Egyptian Hieroglyphs (see Singh, p. 391). However, I looked at this and it does not have anything relevent.
I did find a few other instances of the claim, of which Vincent Cronin (1972) is the earliest. He also gives an explanation for why the scientists were given the nickname (they grew facial hair that fancifully resembled that of the dog breed):
On the strength of his prowess at mathematics, Napoleon had recently been elected a member of the mathematical section of the Institut de France. A month after arriving in Cairo he founded a sister Institut to organize his scholars’ research. He made Monge president and himself vice-president. The Institut met every five days either outside in the shade of mimosas, or in the seraglio of a requisitioned mansion. Napoleon spent so much time there that his army officers became jealous of the ‘Pekinese dogs’, as they called the scholars. For a civilian to be clean-shaven was regarded by the Egyptians as the sign of a slave, so most of the members grew thick moustaches.
Vincent Cronin (1972). Napoleon Bonaparte: An Intimate Biography, p. 153. New York: Morrow.
Like Singh, Cronin does not give references for individual claims, but only for chapters. The references for chapter 10 are on pp. 457–458, and include several primary sources for the work of the Institut, specifically:
I looked at all of these and found no mention of Pekinese dogs. So I do not know where Cronin got this detail. There is a lesson here in the importance of citing individual claims and not just compiling a list of references.