Hi, Robert — a good many families are accounted Norman simply because they arrived in England with (or shortly after) William of Normandy.
I believe the Montgomery/Montgomerie family to be of Norman origin.
But there were also families represented in William’s army that were only temporarily resident in Normandy, since they had been hired by William to build and maintain castles there.
The Bruces (who were Flemings) are among that group.
And the Stewarts were a Breton family, believed to have originated in Cornwall or a nearby part of Britain, which settled, first in England, then in Scotland, following WIlliam’s succession to the English throne.
For centuries the ancestors of the Stewarts were stewards of Dol.
The Sinclairs certainly are of French origin, but whether they are Norman is unclear, since they were part of the group of Templar knights who settled in Scotland following the suppression of their Order in France.
Regards,
Mike