The native Britons are Celtic. You will find their descendants still in their purest form in Wales, Cumbria, Cornwall, Scotland and Ireland.
The Jutes, Angles and Saxons were the first invaders to have any significant genetic impact on the landscape and eradicated the many Celtic kingdoms of what is now called England (Angle-land), including the Gododdin, Durnovarii, etc.
Romans left little in the way of genetics here, but interbred with the locals - I am sure some people in modern England probably have such heritage.
I know that from my genetic testing and the origin of my surname, that my family are from the New Forest in Hampshire, which nearly 1500 years ago would have been a petty kingdom called Ytene, which was ethnically belonging to the Jutes.
Vikings only left their genetic footprint in the North of England in coastal regions, and upon the Isle of Man, the Orkneys and the Hebrides; as well as northern Scotland and the east and north coast of Ireland.
The Normans (who are not french, well, not completely) left also a fairly small amount of genetic material here - however most successful families in this country descend from those ancestors, even a thousand years after the invasion.
The Dutch and French Huguenots have descendants in this country - I know that I am descended from Dutch cloth merchants who made it to Gloucestershire in the early 1500s. But their impact is severely limited generally to the urban hub of London.
The majority of heritage for most British people is going to be a blend of celtic, western european (frankish) and northern european (germanic/nordic).
I hope this helps. Here is my genetic profile for comparison. I post in /pol/, so that accounts for the file name.