While you're waiting for a more specific answer, you might be interested in this older AskHistorians thread: When was driving on the left/right side of the road standardized in countries? How did it develop in the US?
I suspect the main source quoted in it, The Rule of the Road: An International Guide to History and Practice. by J. Peter Kincaid will have some specific information about the claim of Napoleon being the source of right-side driving, although it certainly seems like the reasons for right- or left-sided driving isn't boiled down to just "Napoleon".
The book's not available in e-book form that I can find, nor in any library near me, but perhaps /u/MrDowntown (or anyone else, of course) still has access to the book and can answer you more thoroughly.
As a follow-up, I recall being told that people would ride on the left so they could draw a weapon if necessary (the majority of people being right-handed). Is there any truth to this or is it an urban legend?