When France ceded Louisiana to Spain in 1762, a proviso of the treaty was that France could at anytime request the territory back and that it could not be alienated to another power without French consent.
How about this for a POD?
Perhaps the easiest thing to do is have the French never cede it to Spain and simply remain in control of it. The Duc de Choiseul in 1763 did organise France's largest attempt at colonisation in the Americas to date with the settlement of 12,000 settlers in Kourou, French Guiana. He had envisioned the formation of a settler colony to rival those of the other European powers in America and planned on recruiting and additional 14,000 Alsatians, Rhinelanders and Venetians. He cited the British colonies as his inspiration as they had become a large consumer market for British goods. The lack of preparedness (this was done hastily) coupled with the malarial swamps made it so that the majority of these settlers perished, with only around 1,000 survivors taking refuge in the îles du Salut (Isles of Health) where the strong breezes kept mosquitoes at bay. He also was in favour of taking in Acadian refugees to resettle them in France, with some 4,000 taking refuge in the mother country.
Perhaps if France simply keeps Louisiana and Choiseul decides that France pursue a policy of settler colonialism, they can direct the first batch of 12,000 settlers in 1763 along with the Acadians to Louisiana. Establishing settlements all along the West Bank of the Mississippi River to ward off British encroachment, though at this time there were still few British settlers in the region. If they can continue to recruit French settlers, particularly as the country was plagued by bad harvests in 1769-1770 and 1782-1789, it would not be difficult to have a substantial colony. If government policy is focused on this, at least during the Duc of Choiseul's tenure as minister of the crown, there is no reason that 100,000 European settlers could not be sent to the colony by 1775.
In Western Germany particularly there seems to have been a paucity of land at the time, and that would probably make Alsatians and Rhinelanders along with Swiss Catholics eager to take their chances for free land. In France itself, the government could also recruit settlers during times of famine along with petty criminals such as poachers and people evading the salt tax, using them to settle Upper Louisiana. With enough of an effort, there could be some 350,000 European settlers in the territory by 1789, not an unreasonable number compared with colonisation efforts in Brazil at the time.
Let us assume that the events take place largely as they did in France, without major butterflies. Firstly, the addition of so many more Europeans also adds to the number of African slaves in the territory, making the settlers much more wary of any metropolitan government attempting to ban slavery. Once the French revolution begins, the settlers in Louisiana would probably rebel against the French government in 1793 or 1794, declaring allegiance to the French monarchy. The British of course would be only too happy to intervene to protect the settlers from the revolutionary government. During this period, a well-established Louisiana could take in more refugees, initially from Saint-Domingue, but also from France. It would be interesting to see if a substantial number emigres settle there and the attitude of the Bourbons to the territory. I imagine the settlers would establish a Constituent Assembly in the name of King Louis XVII and later King Louis XVIII, but be resistant to actual imposition of royal rule if Louis decided to send a Governor-General (similar to what would occur in Spanish America later on). If some 50,000 or so emigres can arrive between 1793-1794, mainly lower nobility and or officers they can this new "kingdom" survive. Louis-Philippe (later King) IOTL moved to Philadelphia with his brothers in 1796, it would be possible that he might choose New Orleans instead, in an effort to establish his branch's influence over the country.
The question is, what happens come 1802 when the Treaty of Amiens establishes peace between France and the United Kingdom? In 1802 Napoleon reintroduced slavery in the French colonies, and was able to gain the trust of the settlers in the West Indies as he was more conservative than the early revolutionary governments. However, if Louisiana is a territory of say 500,000 Europeans and some 250,000 African slaves by 1802, would they really trust Napoleon? Also, the British might have made themselves commercially dominant in the area, and despite peace between Napoleonic France and Britain, might want to covertly assist the planters and bourgeois in refusing to recognise Napoleon's rule. This becomes even more problematic with Louis Philippe, who might assert himself as "Regent" or some other title and disobey not only Napoleon but his cousin Louis XVIII.
The border states in the U.S. contained some 300,000 whites in 1800, but these were mainly in the central portions of Kentucky and Tennessee, and for the time being the U.S. still had lots of empty space West of the Mississippi to fill with settlers, so if the Louisiana Government is smart, it can still recruit settlers from Europe to settler Upper Louisiana and have the area safe from American encroachment. Also, by the early 1800s Britain's need for raw cotton makes Louisiana a major supplier of cotton and Louisiana's largest trading partner.
If Spain still goes to war with Britain in 1803, the Louisiannais might take the opportunity to attack Texas during the war of the Third Coalition, as it is sparsely populated and an easy target. This could provoke a crisis in New Spain, and the question would be what the attitude of the British and American governments would be. The British might support Louisiana with arms to attack the borderlands, seeing it as an opportunity to strengthen Louisiana at the expense of Spain. Things could remain problematic and perhaps a peace agreement is reached where territory East of the Colorado River is ceded to Louisiana. Meanwhile up until 1807, when Britain abandons the trade, British slave traders sell thousands of African slaves to Louisiana.
Now if there is a War of 1812, the question is if Louisiana gets involved. Fighting a weakened borderland of New Spain is one thing, but engaging the United States is another. Assuming there are 650,000 whites and another 350,000 African slaves by 1812, they would be more populous than Canada, but still much smaller than the United States with it's 7 million inhabitants. If Louisiana prefers neutrality, it can sit on the sidelines and trade with both powers. On the other hand they probably would not want to antagonise the British as they are dependent on Britain's goodwill. They might also want to support British control over or even divide the Northwest Territory with the British, though this might be a stretch.
If Napoleon still loses in 1814/1815 things might get interesting if Louis XVIII's government attempts to establish control over Louisiana. After two decades of self-government under the auspices of Louis-Philippe, the government might simply refuse. The British would be buying more cotton than ever for cotton to supply the textile mills of Northern England and like the rest in Spainsh America, prefer to have independent states open to trade. Like Haiti in 1825, they might be forced to recognise the Kingdom of Louisiana.
Meanwhile in Quebec the French population's growth rate is continuing unabated. This might make the Louisiana government seek to recruit French settlers to Upper Louisiana from the Lower Canada. IOTL many began migrating to New England in large numbers, but it is possible that they can settle Louisiana along with other Europeans, from predominantly Catholic areas of Germany, Switzerland etc making the white population grow to 1 million by 1825, with the majority settled along the Mississippi River, with New Orleans being a city of over 100,000.
This of course would create several butterflies, as the United States' Westward expansion would be stalled. The country would become denser and probably more focused on industry from early on and making it a much more urban country, similar to a European state in that regard. Without Westward expansion, there is isn't as much worrying about admitting large areas of future slave territory by the North. This might actually cause a civil war to occur at an earlier date.
In France, there might still be an 1830 revolution, but the 10-year old Henri Duc of Bordeaux might become king (under a regency) rather than Louis-Philippe. This completely alters the course of history for France. For Britain, they are probably able to keep the Oregon Territory and whether or not Canada is formed is questionable. It might be possible that one large colony or later dominion consisting of territory West of the Continental Divide. IOTL large numbers of Americans poured into Western Canada in the late 19th century, quickly becoming loyal subjects of the British Crown in exchange for free land. One could see this developing, and having the area that is largely culturally American yet maintaining some cultural distinctions. For Mexico, what happens to the territory they lost to the United States? By 1850 Louisiana might have say 1.8 million whites with some 750,000 African slaves and I can see the French making their moves over the rest of Texas, as Mexican control over the region is weakened and cotton is booming, but not getting California. It might be the British who end up expanding their empire out west at the expense of the Mexicans, and even gobbling up Alaska at some point.
Louisiana remains a monarchy under the House of Orleans, and I imagine that abolition of slavery might come about by the late 19th century, similar to Brazil. Speaking of Brazil, his son Francois married into the Brazilian Imperial family and they might try to support or establish a monarchy in Mexico. The large French-speaking country is home to around 8.5 million whites and another 1.7 million blacks along with perhaps some 200,000 Indians. While not a great power, I would imagine that it would have the same standing internationally as say Belgium, Brazil or Argentina, and still being a British client state, however (much like Argentina) with the Brits investing heavily in railways etc.