Basques and more... 

If anybody knows why Claret is also called Bordeaux and is so popular in England, then perhaps we should include Basques (e.g. Piers Gaveston).  Basques entered English society at the same historic time as the Irish.  I also find it odd that Normans should get monolithic mention, without Brittany.  The Duchy of Brittany was a feudal subdomain of English Kings from the Norman Conquest until the 16th Century, in one capacity or another.  Aside from that, we all know the British (Welsh) connection that practically makes them who they are by definition.  Saint-Pierre and Miquelon has a flag and coat of arms which match English ethnic cousins on the Continent, because virtually all of New France was founded by those "Frenchmen" once under English yoke (north and west coasts of "France").  England's arms supposedly include Aquitaine and Gascony as well as the well-known Normandy.

IMHO:

Normandy has best ethnic transferance with England.  Both Scandinavian.
Brittany has best ethnic transferance with Wales.  Both Romano-Briton.
Aquitaine and Gascony has best ethnic transferance with Ireland.  Celtic/Basque connexions (hmm, Queen Mary's marriage with Spain).

All of these domains were of great post-Conquest importance, with added Scotland under Stuarts.  The union of the crowns under James (after the Tudor-Habsburg struggle) marked the divergence of a merely English people and it is from there, that a new British people was formed with participation in the Dutch and German dominions.  As far as I know and now think, the new "British people" is mostly a network of upper class/parliamentary aristocrats and their personal heritage.

I am proud to sport a 1/8th Aquitainian/Poitevin (although Huguenot) ancestor.  I don't know further genealogy to find a recent Parisian (non-London) French (what is called France, but has English character) ancestor.  You know what side this ancestor would have fought on if Buckingham's war with France got serious.  This opens up a window to the past glories of the Angevin Empire for me because although I sport a Scottish colonial American wife, my own specific heritage does not leave the bounds of the three leopards of the Plantagenet dominions.

What some people should look at, is the French Wars of Religion maps.  Huguenots are numerous in Aquitaine/Gascony and Toulouse, both former Angevin areas.  One wonders if this Protestantism is an Albigensian Crusade relic, an Arian Visigothic vs Catholic Frankish relic or both combined with a culture of English resistance to the Capetians.

Also, if mentioning the Danes we shouldn't neglect the Norwegians.  I think the Royal Website summarizes our English ethnic roots by explaining them dynastically and the personal unions that encouraged a compatible mix of people.  That is why I believe the "French people" are reasonably well related; to nitpick or split hairs on it is just ridiculous.