Looking into the Republic of Madawaska and Brayons how did this area of Northern Maine and Western New Brunswick develop a distinct enough identity to have their own name? Also, how is Brayon culture different from that of the Québécois and Acadians?
Although there are some traditions that place settlement of the region to as early as 1756, the first solid evidence of families settling in what would become Madawaska was in 1784, at least according to George Bible's history on the subject of Acadian deportations. In the period immediately following their settlement, additional settlements were established through petitions in the upper Saint John Valley. Drawn by a relative isolation and pressure from loyalists in the Lower Saint John to sell or leave their property, Acadians settled in Madawaska.
Growing border pressures and interest in the timber of the region by both the United States and Britain led to growing tension, and the so-called "Aroostook War", an undeclared conflict mostly based around militia grandstanding and a boundary dispute over the precise limits of Maine and New Brunswick.
The eventual settlement bounded Maine by the Saint John River and effectively cut Madawaska in twain, but residents maintained ties across the border and until 1870 Catholic parishes on both sides of the border continued to answer to the Archdiocese of Quebec. Settlers came from Quebec as well as New Brunswick, to settle, and Madawaskan migration to the St. Lawrence meant strong ties between the two regions.
We can see the ethnic makeup at the time of the 1843 Webster-Ashburton treaty as thus, a letter from Bible's survey: "It [Northeast Maine] is composed of Acadians and Canadian French, a few Irishmen and provincial Englishmen, and here and there, an American." (131).
The actual Republic of Madawaska most likely never "really" existed, so much as being a way for settlers to proclaim their distinctiveness from both Britain and America and thumb their noses at authorities. It should not be confused with the attempt of John Baker, an American citizen, to flagplant in the region with a few of his buddies and secure the area for America in 1827. His independence struggle got him fined by British officials.
The reputation of the region was mostly for its farming and forestry, and here is where a great deal of the distinctiveness comes from. The economic modes of the Acadians living in New Brunswick (many of whom would sometimes seasonally migrate to better opportunities or else emigrated altogether from the county) were decidedly rural. Rev. Charles W. Collins from the Portland Diocese calls it "backwards", and while I don't think I would use such blunt terminology, it was certainly a sleepy region (Madawaska Tourism, please send your cheque to P. Sherman, 42 Wallaby Way Sydney).
Brayons still hearken back to their Acadian and Quebecois heritage and shares cultural links with both Quebec and Acadia, but it has a different dialect and a different history; it's a regional identity borne out of a unique heritage and economic conditions.
Main source on the matter in French:
“Histoire du Madawaska entre l’Acadie, le Québec et l’Amérique" by Thomas Albert, edited in 1982 and republished by Adrien Bérubé, Benoît Bérubé and Georgette Desjardins
An English source for the origins of Madawaska county:
The Acadians: Their Deportations And Wanderings by George P. Bible