This seems as if it would be very difficult. Even if the Saxons wanted to utterly remove themselves from their homeland (and, mind you, there were a lot of Saxons.), and Saxony isn't terrible land by any means of the imagination, you still run into two problems: 1) The Saxons were a tribal Republic with an aristocracy which was very jealous of their power, and so it is unlikely that a single strongman would be able to entice the entire group to up and move. 2). The Franks are in their way, and if they were able to drive the Franks out of Gaul, why settle to only settle in Normandy when there are better lands available?
And 3, some Saxons did (hence why both sides of the channel was known as the Saxon shore) - they were either absorbed by the Franks or joined the Saxons in Britain as Jutes.