Those days, monarchs generally didn't care a lot what language their subjects spoke. The reverse is also true: the general population usually hadn't a lot of problems with the language their rulers themselfs spoke and a lot of times accepted that central administration was deat with in another language (which was most notably the case in France).
France is a case in point: monarchism stood very strong in Brittanny, despite the great majority of its population at that time either speaking a Celtic language or a rather divergent langue d'oïl called Gallo. So whether or not the Corsican people at the time spoke Corsican (and whether or not that is to be seen as a form of Italian), French or another language isn't that important. However, would it really be feasible for Marie-Antoinette to rule an island, very close to France's mainland? I would assume that strong interrnational military support would be necessary, also considering the fact that the island had only 20 years before that become part of France (and very reluctantly, if one may say so) and was also the birthplace of Napoleon? One would guess that, without foreign military support, the Corsicans would at least as easily get rid of a weak Marie-Antoinette as they got rid of revolutionary France in OTL in 1794.
As regards the linguistic situation in Flanders during the Burgundian era: it's no doubt true that the majority of the people in the County of Flanders spoke Dutch, but it should not be forgotten that Flanders contained considerable area's where French (or at least a langue d'oïl) was spoken and that - no doubt helped by the fact that it was a French province - French was an important elite and administrative language. Between 30 and 60% of all pre 1500 documents that can be found in the city archives of important Flemish cities such as Ghent, Bruges and Ypres were in French.
The contrast with Brabant couldn't be greater. French documents are almost nonexistent even in the city archives of Brussels, right up until the end of the Ancien Régime, the exceptions being mainly correspondence with foreign dignitaries and with those limited parts of Brabant which were French-speaking as well as certain proclamations by the Habsburg governors on issues not solely related to the City of Brussels. Of the 3 039 ordonnances made by the Brussels city administration between 1635 and 1793 (as can be found in the city's "publicatieboecken") only 10 were in French. Not being a French province and with only small areas speaking French, the French language didn't play an equally important role in Brabant. Not that it didn't play a role (it certainly did at the Governor's court), but not to the same extent as it did in the County of Flanders.