Also, update: I have figured out how to use that button that looks like a paint can,, so my update schedule will hopefully become more regular as previously I was just colouring every individual pixel and this was quite laborious at times.
The Beaulieu Islands were not named by their discoverer, Agustin de Beaulieu, the French explorer who discovered them in 1621 after getting thoroughly lost in the boundless Pacific Ocean. In fact, Beaulieu thought that they were part of the Great Southern Continent, and only mapped the western portions before returning to the East Indies. He dubbed the land 'Louisiane', which obviously became very confusing when Louisiana was named a few decades later. As such, once later explorers discovered the truth about the new lands, they settled on calling them the Beaulieu Islands - his original names for the individual islands, however, stuck. Bishop's Island is in the South, named after then-future Cardinal Richelieu, whose approval Beaulieu sought for grand feats of colonising fervour, and Montmorency Island, after the patron of Beaulieu's voyage.
Bishop's Island, now the overseas département of Quailletahu, remained in French possession until the present day, and is a major source of dairy products for the metropole, ever since the island's settlement was pursued by Bougainville. The northern island has had a more complex history - in 1651, it was sold by the French Compangie des Iles de l'Amerique, the mercantile company which owned both islands at the time, to the Knights Hospitaller, a Catholic military order which was originally founded to maintain Christian rule over the Holy Land, but after failing in that objective, continued in existence as the rulers of the islands of Rhodes, and then Malta, fulfilling their military purpose by attacking Muslim-owned shipping every now and again.
The sale to the Order was part of a job-lot, with the big ticket items being a few productive islands in the Caribbean, which were subsequently sold to France itself when the Order realised how expensive it was to run a colonial empire. France, though, had no interest in buying Montmorency Island for any price, and the Order of Malta retained it for another hundred and fifty years, spending no money and even less thought on attempts to convert the Barbaric Natives or make any money out of them.
That is, until disaster struck. In 1798, the island of Malta fell to Napoleon after a short siege. The Order had no sovereign territory left apart from Montmorency Island, and the French Revolution had denuded them of their vast private estates in that country. The Knights were spread across Europe, but some of them, led by the Italian Bartolomeo Ruspoli (then in exile in Scotland), organised a trek of Order members and adventurous civilian volunteers, to take possession of their forgotten Pacific land. After several years of confusion in which the married, Russian Orthodox Emperor Paul of Russia was elected Grand Master by one (fairly desperate) faction of Knights, Ruspoli was appointed Grand Master by the Pope and the trickle of Order veterans and Catholic lay missionaries became a flood.
Ruspoli's first settlement was in the Baia del Delfino, among a friendly tribe called the Ngapuhi. The area, which was relatively densely populated, offered safe harbour, and was already visited frequently by sealers and whalers, was bought by the Order in exchange for Catholicism and vast quantities of muskets, which had two effects. Firstly, Ruspoli was able to build a new capital Nuova Valletta, and secondly, the Ngapuhi were able to raid all of the neighbouring tribes, who thought that this was quite unfair and decided to embrace Catholicism and the Order so as to get some of those awesome musket things.
Such was the start of the current phase of the history of the Knights Hospitaller. Unlike other examples of European colonisation, the Order didn't have a huge surplus population in their metropole - indeed, they had no metropole, and mainly relied on immigrants from Southern Italy and Ireland during the 19th and 20th centuries. Hence the organised crime syndicates that run rampant in the capital and port city, Tamacchi, and the hardy farming folk who tamed the Transtararuia. Due to the limited migration from Europe, incomers were never able to outnumber Maori, as the French did on the southern island, despite the huge impact of European diseases and the occasional religious war perpetrated by the order on recalcitrant Maori tribes who just happened to have some land that the Order wanted.
Today, the Order of Malta occupies only a minority of the island, and is governed spiritually by its Grand Master, who reigns from the Magisterial Palace in Tamacchi, over the water from the Forte Santa Vittoria, and is elected by the celibate, noble Knights of the Order. Temporal authority, after a great deal of domestic dissent, was devolved to a democratic system in the 1930s: all adults are enrolled in one of the Langues of the Order, even if they are not religious, based on various factors including their racial background, class and occupation. Every Langue elects ten members to the Grand Council, irrespective of how many electors are in each Langue, and the members of the Grand Council (who are formally Independent) then elect a Grand Commander (equivalent of a Prime Minister) from among their own number. This system has been described by Human Rights Watch as "taking the fucking piss".
As the Order was never able to dominate the whole island, Maori countries occupy the rest, having emerged from pre-Order tribal structures. In the North, Ngapuhi cowed the surrounding tribes and formed Te Whakaminenga ('The Confederation') which is formally a constitutional monarchy, but follows the usual Pacific democratic tradition of voting for the most high-born candidates on offer. The leaders of all three parties are first cousins of one another. South of Tamacchi, meanwhile, the Tainui tribe spent most of the 19th century building power over the other tribes of the more sparsely populated main portion of Montmorency Island. They are formally an absolute monarchy, again with a uniformly chiefly political class. The Tainui-led state is called Te Karanamaitiratanga: 'Karanamaitira' is the Te Reo Maori form of 'Grand Master', which has come to mean any sort of supreme ruler - for instance, David Duke is Karanamaitira of the USA.