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?