@ DrakeRlugia: well whether Burgundy was an appanage was contested between France and the house of Valois-Burgundy and the successor the house of Habsburg. Certainly the duchy of Burgundy held by the Capetian house of Burgundy wasn't an appanage, in fact they even had the right of succession from/through the female line in absence of a male heir.
Maybe Anjou, Berry and Orléans are less contested examples of appanages.
Appanges are a little more fluid in the early modern era; it wasn't until the the Estates at Blois codified things more clearly in 1566 regarding royal lands: that they couldn't be alienated, sold off, and ecetera, and appanges could still be granted, but were to be reunited with the royal domain in the absense of a male heir.
The Duchy of Burgundy was an appanage in the sense that it was part of the crown of France, annexed in 1004. Typically as the French kings expanded their base of power, so grew the royal domain. Burgundy was granted firstly to Robert, son of Robert II of France to settle the succession dispute, and was a Capetian as you said. The Duchy of Burgundy ruled by the Capetian Burgundians wasn't an appange in the traditional sense in that it was not granted by the king to a son or grandson, but was granted to settle a dispute with no stipulations attached to it often were with typical French appanages. The Capetian Burgundians
were French vassals of course, but acted quite independently, and at least until the 13th century were more powerful and more wealthy. This line ended with Philip of Rouvres, who died at fifteen. From 1032 to 1361, they had ruled the Duchy in an unbroken line of male succession.
After his death, the reigning King of France Jean II successfully claimed the Duchy as the closest heir by proximity of blood, most obviously through the female line, but I'd argue his position of King of France was much more important. The House of Valois-Burgundy were granted Burgundy as a traditional appange. Their expanded their territories through various marriages, yes, gaining places such as Franche-Comté, Artois, Hainault, Holland, and Flanders, some territories which were fiefs within the kingdom and others were not. Charles the Bold's death gave Louis XI the opportunity he needed to reclaim the original territories that Jean II had granted to son Philip as an appanage. As they had been granted as such, legally they would return into the hands of the crown; the other territories acquired by the Dukes, be it through marriage, purchase, ect., would not, because they had not been granted by the king.
The big issue whether Burgundy is or was not an appange primarily comes from Philip of Rouvres will, where he stated that his "county, and to our possessions whatever they may be, those, male and female, who by law or local custom ought or may inherit." Because Burgundy by this time practiced simple primogeniture there was no way all of the territories would pass to one man or woman. All of Philip's territories had passed to him in different ways, which meant they would be inherited in different ways accorded to the customs of each of those fiefs: Auvergne and Boulogne passed to Jean de Boulogue, Philip's great-uncle; The County of Burgundy (that is, Franche-Comté) and Artois passed to his great-aunt, Margaret of France.
Burgundy was more complicated. Two succession laws were held as valid. Primogeniture, which is based on a line of succession, such as a grandson succeeding his grandfather as king because his father and the original heir had passed, rather than the king's second son, the grandson's uncle. The other was proximity of blood, such as in Artois where Robert II's death saw Mahaut, his eldest daughter succeed, rather than his grandson by his eldest son who was deceased.
Essentially, the actual Duchy had a super complicated succession issue because of overlapping laws and wills, and the two claimants more of less had equal right to claim Burgundy: the King of Navarre or the King of France. In the case of the end of Capetian Burgundy, it seems a case of 'might makes right' more than anything. Capetian Burgundy was definitely not an appange, but once it was taken by the King of France and given to his son as one, it was. But
only the Duchy proper. The Free County was part of the empire, as were the acquisitions in the Lowlands. While Louis XI had a right to annex Burgundy (even if it was a low blow and dirty move: but hey, he's not the spider king for anything) he knew he had no right to the entirity of Mary's inheritance, hence his poor attempts to have her marry the Dauphin, his nine year old son.