Most people are right-handed and it seems natural that people used the left hand side of the road when riding horses or simply walking. In case of conflict a weapon could be easily put between you and the opponent.
However, I've read the change to drive on the right is due to Napoleon. How accurate is this story? What's the real origin of the move?
I have been doing some (online) research on the issue.
What is clear and factual is that when Napoleon conquered most of Europe he set a lot of standards in the Conquered region. From driving on the right side, common measurements/weights to require people to have a last name. So this should be your answer already. All other countries driving direction can be easily found and were documented, mostly because of kolonial/trade influences.
But, the whole story that Napoleon forced France to drive on the right side because he was left handed, an outcome of the revolution or as a statement against the church (because it is also believed -yet undocumented- that there was a Papal degree in 1300 making people keep to the left)
I believe the true answer to your question lies in the research of an the author Peter Kincaid who wrote The Rule of the Road: An International Guide to History and Practice, in which he answer the question:
Did France change sides of the road in rebellion against papal authority?
Probably not. This is a common belief, but Kincaid, besides refuting the existence of any papal order pertaining to the rule of the road in Europe, finds no evidence that left-hand driving was ever common in France. It appears likely that France has always driven on the right. Nicholas Hodder reports a rumor that some pre-Napoleonic pictures show traffic travelling on the left of the Champs-Elysées, but I have yet to confirm this.
source: Brian Lucas: Which Side of the road do they drive on?
Richard F. Weingroff at the US Department of Transportation, in his article On The Right Side of the Road, investigated this in the context of why British colonists in what became the USA chose the opposite driving side to their homeland.
He determines that the US practice of driving on the right derives from two colonial practices - driving large vehicles such as the Conestoga wagon and carrying firearms.
He explains that Conestoga wagons were large, wide vehicles driven by two lines of horses, and right-handed drivers typically rode on the rear left horse in order to maintain control (via a whip held in the right hand). Because of the width of the wagons, it was difficult to pass and so drivers seated on the left would choose to pass on the side that allowed them the most visual clearance, which would be on the right.
This practice of driving on the right was codified into Pennsylvania law in 1792 for the Philadelphia-Lancaster Turnpike (present-day US Highway 30). Traffic was affirmatively required by law to keep to the right rather than choosing the most expedient passing side based on context or situation.
Weingroff also observes that the widespread practice of carrying firearms in Colonial America also contributed to traffic passing on the right. Since the majority of the population was right-handed, typical firearm stances would make it easier to shoot slightly to the left than to the right, so people kept to the right in order to prepare to defend themselves against potentially hostile oncoming traffic.
