Alright the town and name Orange found its way into Dutch history through hereditary processes. Rene of Chalons used to be Prince of Orange until his death in 1544. He left Orange and several possessions in the Netherlands, then ruled by the Habsburgian Charles V, to his cousin William of Nassau. This William would therefore found his own branch of the House Nassau, the House of Orange-Nassau. William of Orange Nassau would become the leader of the Dutch revolt against Spanish/Habsburg rule and his descendents became hereditary stadtholders and later kings of the Netherlands.
The Dutch translated the French Orange into Oranje, hence the affinity with the colour.
I would not say, by the way, that the town was fundamental to Dutch history. It gave William of Orange-Nassau his name and higher standing before he gained more titles and lands through marriage, but beyond that it did not have a significant role in Dutch history.
Hi, hopefully someone can drop by with a comprehensive answer, but you can get started with some earlier comments
Though the Popes left Avignon after Pope Gregory XI, Avignon remained under Papal control until the age of Napoleon. What might life have been like in Papal Avignon in its last century of existence? /u/mormengil gives a quick overview
Why did the Dutch golden age end? /u/PietjepukNL goes into more detail
Why do the Dutch (Netherlands) have such an affinity with the color orange?
Question to the OP: what gave you the impression the town Orange is fundamental to the Dutch? I know we have the house of Orange (Oranje) and the color is of importance, but that is what I know of it as a dutch guy. This is the first time I heard of the existence of this town.