Highlander
The key point of those 3 is continued peace with Britain. Although as some posters have said that basically means a radically different Napoleon. If he doesn't have a lasting peace with Britain then Louisiana falls, either to Britain or the US.
The other two are less important. Would be far more possible if either Dessalines dies and the rebellion in Haiti collapses or probably better Napoleon decides to recognise the slaves as free, which would cause tension with other powers but avoid the costly battle that occurred OTL. Otherwise he will probably have to send more troops to guard Louisiana, although that is not too great a problem if he decides to avoid war with Britain.
Peace with the US is far less of a problem. Provided he has peace with Britain Napoleon can easily reinforce Louisiana and threaten/attack the US main coast if it causes problems. The latter would be suicidal to attack France under those conditions.
Similarly I am dubious about the US flooding the region with settlers. With the exception of Texas US westward expansion was militarily led with the army clearing the land for the settlers. This will not work west of the Mississippi as the Indians on their own will be able to handle most settler intrusions and the Americans are going to have to build and maintain a [for them] huge army to fight France. [Both to have something struggle overland to seize areas and to try and defend the coast and their main settlements against the blockading French forces].
The difficultly is having a lasting peace between Britain and France. Possibly Napoleon decides to expand in the Americas by settling and securing Louisiana, although in the longer term that could cause problems with the locals. Or even he dies off and a more responsible leader takes over France.
Steve
I'm not so sure about your thoughts on a Franco-American War. For that war, the War of 1812 would seem to be a good baseline (major European power vs. US). That war ended in a stalemate and Britain had far more advantages (larger navy, Canada as base, etc.).
France will be fighting very far away from home and the only major city worth defending (New Orleans) is extremely close to the border. While teh war might eventually end up in the stalemate, I wouldn't describe it as suicidal for the Americans (who will also be doing well since New England won't be as damaged economically).
The other factor is if Napoleon gets bogged down against America, the other European powers will probably come after him, and then he's in trouble.