The British and French both had inches, but they were different sizes. A French inch was longer, so when Napoleon was described as 5'2" (which as far as the French were concerned using their measurements, made him normal sized), the Brits heard this and thought that it was in their inches and that Napoleon must be tiny. In fact he was slightly above average height for the time.

He was also commonly seen by his men surrounded by his bodyguards, who were all required to be tall, which would make him look small in comparison.

It also played out as a way of slandering Napoleon, and taking away from his figure, if you could make people think he was tiny. And as the saying goes, a lie is halfway around the world before the truth has had a chance to tie it's shoelaces.

https://www.thoughtco.com/was-napoleon-bonaparte-short-1221108

https://www.khanacademy.org/questions/how-tall-was-napoleon/kafb_3348560 This link gives details fo the differences in French and British inches;

The French inch of the time equalled 2.71 centimetres, while the Imperial inch is 2.54 centimeters.