Well, to be nitpicky, New France proper wasn't ceded to the US - it was taken by the British after the battle of the Plains of Abraham... and is now part of Quebec.
But if Napoleon never sold the Louisiana territory to the US? Then eventually there would have been a Franco-American war: "Manifest Destiny" and all that would've brought the US to invading the French territory.
Assuming the War of 1812 went as it did, and the American invasion of Louisiana happened after that - say, the 1820s or 1830s - then I could see the French getting British assistance against the Americans, as with a second war being started on the continent by the Americans, the British/Canadians would start viewing the US as an even greater threat than before, and either removing the threat by conquering the US or bottling it up such that they have no room to expand westwards.
Scenario: The US invades Louisiana, France resists. Britain evaluates the situation, and determines that it is not in the Empire's interests to allow the US to acquire that territory. So, the RN heads out to blockade American ports, while crossing the river to capture Detroit, and probably making other invasions, into Maine and/or upstate New York. The US at this point is forced to rely entirely on itself - France was probably its most important supporter, but by invading French territory they shot themselves in the foot, while Prussia would be simply unable to get any supplies to the US - either their fleets get bottled in at the Skaggerak or the Channel, or they can't get past the RN blockading the American ports.
Britain and France, however, are in a very good position here. Even if the Americans are able to hold out for a time, their resources will start to dwindle, whereas the British and French have their supply routes pretty well completely open and thus can simply wait the Americans out.
Sooner or later, it gets to the US having one of two options: fight it out until their territories end up split between Britain and France and be removed from the map completely (Option A), or sue for peace, make some territorial concessions (south shores of the Great Lakes going to Canada, for example), but remain independent (Option B). Any fantasies about manifest destiny would, of course, have to be given up.
Option A: the US fights to the bitter end, eventually its entire territory is occupied by Britain and France. All the important political figures are removed... in the British-held territories, the exiled Loyalists return, being given back whatever they lost and perhaps more. There may well be some form of guerrilla resistance happen for a while, but eventually, that will subside. The race for the west is now a three (maybe four)-way thing between Britain, France, Spain and maybe Russia. Of course, no Civil War as such, and the 20th century would be vastly different...
Option B: the US sues for peace, making some territorial concessions (upstate New York along the St Lawrence River to Canada, along with Michigan and maybe some other bits, Mississippi to France, maybe... not that important right now, though). But the important thing is, the US continues to exist, if in a smaller form, and without the room to grow into a major power. If a Civil War were to happen, it may be more likely that the two Great Powers get involved. I could see a number of interesting scenarios there - Britain and France both support one side or the other, or each supports one and it turns into a Britain vs France war fought on US territory, or both sit aside and wait to see what happens, perhaps to pounce on the ruins afterwards. Given this, though, I think the Americans would think much harder about starting such an internal conflict, as the worry about /two/ great powers right on their borders would give pause. So, assuming no civil war happens, the 20th century is still vastly different. The US is certainly a significant regional power, as is the Republic of Louisianne, Mexico is likely much larger, Texas is an independent state, and Canada is much as it is now, perhaps with the addition of Alaska. I'd say in modern times the US would have the significance about equivalent to that of RW India in modern times - a very important player in American affairs, not one to ignore on the world stage either, but not one of the Key Players.