The only credible information I know of about the history of the Vaus or de Vaux family at the time of the Norman conquest of 1066 is from the book “The Anglo-Norman Era in Scottish History” by G.W.S. Barrow which suggests that the family was not of great distinction at this time.
Playfair in “Baronetage of Scotland, (quoted by Balbirnie) and Balbirnie in his “Genealogical and historical account of the family of Vance” claim a connection with the lords of Baux, in Provence. To my knowledge there is no documentary evidence to show any such link or any reason to suppose that there is any truth in the idea. I believe that the heraldic evidence shows clearly that there is no such connection.
~Jamie Vans of Barronbach
The de Vaux/Vans origins These Vance families are either Irish or trace their surname to original immigrants from Ireland, where "Vance" has been mainly a Protestant name in Ulster since the 1600s. The generally accepted origin of Vance in Ireland is from Scotland where the name was Vaus or Vans. In 1860, a Scottish genealogist named William Balbirnie published a book that tied the Irish Vances back to a Rev. John Vans/Vance who lived in Kilmacrenan in county Donegal in Ireland, and connected him to a Vans family of minor nobility in Barnbarroch, Scotland. The Vans of Barnbarroch have ties back to the medieval de Vaux family who came over to England from Normandy with William the Conqueror around 1066.
"de Vaux" was a Norman French place-name meaning "of the valleys", and although their exact origin in Normandy is unknown, the story of the de Vaux family in England and Scotland is fairly well-documented from the 11th century onward. Legend ties the de Vaux family to the French/Italian de Baux family who themselves claimed a family tie back to Balthazar, one of the Magi Kings, but there remains no proof of any of those connections.
Modern DNA testing has suggested that the origins of the Irish Vances is not as simple as that proposed by Balbirnie, although one group of modern Vances has confirmed ties through DNA to the Vans of Barnbarroch and so to this general ancestry. Whether the story is completely accurate, and whether other Vance family groups who trace their lines to Ireland have the same surname ancestry (as opposed to genetic ancestry) is unknown at this time.