Which French rifle was it based on? Simon is correct that the EM2 was adopted, so I was a century out
Well, not rifle itself (it is hard to find originality in the muzzle loaded percussion "rifled muskets"), but a Minie style bullet, or more exactly Boxer's modification of it.
As for EM2, sure was adopted but did not really see any service so it does not count.
For Brown Bess, everyone at a time copied Dutch (they were The Gunsmiths of the Europe at one moment) including Prussians, French and Russians, but with flintlock rifles it is even harded to tell what was original and what was borrowed due the extremely simple mechanism compared to a later weapons.
Then there are revolvers, where British lead a world for a while (Adams and Tranter were both light years above Colts of the same period), but decided that further technical development was not needed and kept same 1880s construction until WW2... But it was as British as it could be.