William II
As the successor to William I, William Rufus' story is relevant to the local history as the division of land post conquest had land-owners on both sides of the channel.
William Rufus' death in the New Forest is seen as suspicious as it could have been an accident or possibly murder. The later could be explained in that he was "at odds" with many of Norman Lords with possesions in Normandy and England including his uncle Odo of Bayeux.
The Wikipedia page says:
Anselm of Canterbury
William Rufus appointed Anslem, then a saint, to archbishop of Canterbury
A monk and abbot of Bec Abbey (in the Bec valley midway between the cities of Rouen and Bernay).
Lanfranc
Lanfranc, OSB (b.1005 to 1010 – d.24 May 1089) was a celebrated Italian jurist who renounced his career to become a Benedictine monk at Bec in Normandy. He served successively as prior of Bec Abbey and abbot of St Stephen's Abbey in Caen, Normandy and then as Archbishop of Canterbury in England, following its conquest by William the Conqueror.
Archbishop Lanfranc opposed the non-canonical marriage of Duke William with Matilda of Flanders (in 1053).
St Stephen's Abbey is also known as Abbaye aux Hommes (Caen).
John Gillingham - The lives of the Kings and Queens of England - edited by Antonia Fraser
John Gillingham is the author of the sections of "Kings and Queens" on the lives of William I, William II, Henry I and King Stephen.
Robert de Mowbray
Split Loyalties
Many of the "new English lords" were also Norman Lords and had property on both sides of the English Channel.
As William I was not actually in the country and he was not only having problems with his eldest son.