Very interesting topic, as I love the dualism between the "two Burgundies", i.e. the Duchy and the County (aka Franche-Comté):
Gilbert of Chalon,ancestor of René of Chalon,who proclaimed his cousin Willem of Nassau his Heir
No doubt this Gilbert of Chalon, Duke of Burgundy (952–956) was a cognatic ancestor of René de Chalon, but agnatically the House of Chalon-Arlay was a branch of the House of Ivrea, once Kings of Italy and Counts of Burgundy.
In the 13th century they came to occupy a strategic position along the river Sâone, roughly the dividing line between the Duchy and County of Burgundy, when Etienne III, Count of Auxonne, married the heiress of the Count of Chalon-sur-Sâone. Their son Jean I (1190 - 1267) was not just the first Ivrean by the name of Chalon, but also founded the dynasty's position when he allied himself with the Duke of Burgundy and exchanged the border counties of Auxonne and Chalon in return for great landholdings in the County of Burgundy: The rich salt mines of Salins(-les-Bains), Belvoir, Vuillafans, Ornans, Montfaucon, Chaussin, Orgelet, Arlay, the Château des Clées in the Vaud and other important strongholds protecting the transport of the precious salt mined in his mines.
Even though they kept their Chalon name, their new arms was those of the Barony of Arlay (still one of Queen Beatrix' titles): Gules, a bend or, which they later quartered with the hunting horn of the Principality of Orange and the chequered gold-blue arms of the County of Genevois over-all. Hence they were also known as the House of Chalon-Arlay.
The Chalon-Arlay arms in the arms of Willem the Silent (over Nassau, Katzenellenbogen, Vianden and Die(t)z):
Very interesting with regard to the later Nassau-Orange - Coligny alliance is also the fact that the Chalon-Arlays, both as Counts of Chalon and Lords of Salins were among the great Burgundian feudatories who ranked as Princes of Burgundy, together with the Princes of Coligny. Coligny being a village in the County of Burgundy, in the so-called Sovereignty of Revermont.
And the Coligny arms (left) seem to be a variation of the ancient arms of the County of Burgundy (right):
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While the modern arms of the County of Burgundy aka Franche-Comté (left) down to the field "billetty or" are strikingly similar to, even identical with the Nassau arms (right) and thus also to a large extent with the modern Dutch arms, even though they as far as I know evolved independently:
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