The question and answer site Quora has this piece which makes rather interesting reading, so I have copied and pasted it, with occasional minor typographical emendations:
"Who were the ancestors of the current British Queen, the French or the Germans?"
Michael Ruby, a researcher in the field answered on November 18th last year:
Before considering the ethnic background of her ancestors, I want to explain an aspect of Her Majesty’s genealogy that may surprise you. She is mostly non-Royal. If we group her 2,048 11th generation ancestors, as William Addams Reitwiesner has, we find 1,254 non-royals (~61.23%) and only 794 royals.
I’ll discuss the royals shortly. For right now, suffice it to say that it is very difficult to devise a consistent way to assign an ethnicity or nation to historical royals. They moved around a lot. Borders moved around a lot. Also, their known ancestry long predates the concept of the nation-state, so even a consistent method will be wrong.
It is therefore useful to work backwards in time, looking first at how non-royals became ancestors of royals in the 20th century, then following the same trend back for many centuries.
The nationalisation of the Firm:
794 out of Elizabeth II’s 2,048 11th generation ancestors were English, including quite a few from English background who lived in the North American colonies. 160 were Irish, including Anglo-Irish. Also some Scots.
These ancestors come entirely from her mother’s side. Before she was HM Queen Elizabeth The Queen Mother, she was Lady Elizabeth Bowes-Lyon. Her marriage to the then Duke of York was reflective of an understandable post-World War mood in Britain--to stem the "foreignness" of the Royal Family.
The plan basically worked, and while there are still people who irritatingly point out "Actually, They’re Germans!", it’s not nearly as bad as it would have been had the royal houses of Europe kept on marrying each other for another hundred years. Imagine a Brexit-like vote in a world where the Queen spoke German natively and there had just been a royal wedding between the young British heir and a Romanian princess. "Leave" might have been a republican movement.
As it stands, Prince George and siblings are about 78% British, as the ancestry from Diana, Princess of Wales, and the Duchess of Cambridge are nearly 100% British. Diana had some Armenian, though, and perhaps Gujarati.
Wealth, fame, sex, alliance: Royals have always married non-royals
Now to the non-British, non-royal ancestry.
Here are the complete ancestry percentages for Elizabeth II, according to Reitwiesner:
38.769 531 25 % English
38.769 531 25 % Royal
6.25 % Anglo-Irish
6.25 % Hungarian
3.759 765 625 % French
2.880 859 375 % German
1.562 5 % Irish
0.439 453 125 % Dutch
0.439 453 125 % Scottish
0.292 968 75 % Danish
0.244 140 625 % Belgian
0.244 140 625 % Swedish
0.097 656 25 % Bohemian
See any surprises?
128 were Hungarian, ancestors of Claudine Rhédey von Kis-Rhéde, paternal grandmother of Queen Mary--George V’s consort. All of Claudine’s known ancestors were from the Hungarian nobility, primarily in Transylvania.
77 out of the 2,048 were French and 59 were German–all various wives and mistresses of royals, all with mostly non-royal ancestry.
So is the Queen really only ~3.76% French and ~2.88% German? Again, it depends on how we interpret the royals. These are specifically the non-royal French and non-royal German.
A lot of the French consists of the repeated ancestors of Eleanor Desmier d'Olbreuse, a minor noble who married the heir to Brunswick-Lüneburg and became the maternal grandmother of George II. The German ancestors have parallel stories--as do the Dutch, Danish, Dutch, Belgian, Swedish, and Bohemian commoners in her ancestry--basically minor noble women or army officers with little to no royal ancestry, who became associated with royals in much the way that non-royals do today, with wealth, fame, and sex.
Is "Royal" an ethnic group?:
Reitwiesner argues that "Royal", while not an ethnic group precisely, should be treated like one genealogically,
The only way they differ from other ethnic groups is that they are not geographically discrete, but in other respects they meet all the qualifications of an ethnic group: their shared rituals, their shared language(s), etc., and (most significant from a genealogical / genetic perspective) their mating habits. Until fairly recently, the only acceptable mate for a Royal, male or female, was another Royal. Royal = non-Royal matings which resulted in Royal offspring are notable primarily for their scarcity. For this reason, I have described someone whose ancestry is exclusively or primarily from this Royal caste to be of the "Royal" ethnic group. 
He goes on to say that if you don’t accept this notion, you can lump them in with the Germans. That would make Elizabeth II ~41.6% German, so, barely more than she is English, and not a majority.
I don’t agree that it can be called German, for two main reasons.
First, note that Reitwiesner’s numbers stop after Generation 11. That was, admittedly, enough work already. He showed that the 17th - 20th centuries all had a small steady influx of non-royal ancestry into royal families through major noble intermediaries. But there’s no evidence that this began in the 17th century. In fact, for a few regions of Europe, we know this was more common before the 17th century. Notably, in Britain itself.
While the Hanoverian Georges were quite German, Queen Anne and Queen Mary II had an English commoner mother, the Stuart/Tudor-allied maternal lines go primarily to Scottish and Welsh families of minor importance, and the Wars of the Roses saw the need for internal political alliances overwhelm any need for Continental relatives. Similar phenomena struck most European regions at various periods of internal strife--and it was always dominant in areas like Scandinavia and Poland where monarchs tended to be elected.
Reitwiesner lists George I of Great Britain as entirely Royal, which is not quite right. He was descended from Lord Darnley, husband of Mary, Queen of Scots, who had some royal ancestry but was primarily Scottish nobility. George was also descended from
Jacqueline de Longwy, of French noble (but not royal) abstraction. Also those Welsh Tudors, and some Czech commoners, long before his own 11th generation.
So Reitwiesner’s ~38% Royal number for the Queen is a bit of a high estimate. More non-royals come in the further we go back in time. Of course, some of those commoners in her mother’s ancestry wind up having a minor amount of lines (a millionth or so) coalescing back into royals, but not nearly as fast as royals accumulate non-royal ancestors.
Like Mary Towneley [Warner], ancestor of Elizabeth Bowes-Lyon (and George Washington) who is descended from William I The Lion of Scotland. The Queen is descended from previous British royals through royal lines of course, but also through non-royal lines.
So the idea that a 19th century Western European royal descends only from 9th century Franks--essentially, all lines back to Charlemagne--is preposterous. Royal percentage fluctuates over time, but probably rarely approaches 100% in an individual.
Of course, 19th century royals did descend overwhelmingly from various early medieval kingdoms in and surrounding Charlemagne’s empire--including the Franks themselves and in marks from Spain to Italy to Lusatia. That idea does support a "Royal" ethnicity or caste. I don’t think it works to call the group "German". The people involved didn’t have that national identity, and were not limited to the bounds of what Germany is today. Post-Roman Germanic, including Franks, Saxons, Visigoths, and Lombards? Maybe.
But the exceptions make it quite likely that Elizabeth’s "German" proportion is well below her "English" proportion.
One last note. The reason you probably assumed French or German:
You’re likely thinking of the small but politically significant 1536870912 of her ancestry that is her direct royal line from William the Conqueror--or perhaps of the medieval period where French and English crowns intermarried frequently. While that line is one of the two reasons she has her crown (the other being Parliament), it is not more genealogically significant than the 536,870,911 other lines of that generation, or than the 1,000,000 or so known other lines from Elizabeth II to William I.
German? You may be confusing ancestry with patrilineage. While the House of Windsor was once the House of Wettin (via Saxe-Goburg and Gotha), the route of one’s father’s Y chromosome is hardly the only thing in ancestry.
It’s neither of these.
A person’s ancestry consists of the complete set of individuals to whom the person may be connected, tracing backward in time, by a series of 1 or more child-parent relationships.
As we see above, that’s way more complicated. And way more fun.
 The Ethnic ancestry of Prince William
 The Ethnic ancestry of Prince William
 Ancestors of American Presidents: Gary Boyd Roberts: 9780936124148: Amazon.com: Books