There are about 150 places called Beauregard in France. The Beauregard name is usually given by the local geography. It designates a promontory allowing to have a beautiful look over the surroundings. It is thus not surprising to find many Beauregard Castles, for example, and many gave their name to wines.
Davignon is likely formed from the name of Avignon in the South of France. D'Avignon litterally means "from Avignon". It is thus quite possible that the first of that name is from Avignon, or that his ancestors were living there. But we don't know more.
I found 1390 Davignon, most being descendants of François, but it seems a specialist of that family found 2500 of them, most being located in USA.
(C) Copyrights 1999 Denis Beauregard