So before I start an excellent book on this is Reversing Babel by Dr. Bruce O'Brien. It covers exactly this subject.

So there are a few important pieces you're missing. First, the battle of Hastings. In this battle the Anglo-Saxon nobility was decimated had the day been won in their favor there still would have been a dearth of nobility. Now what about after the battle?

In thanks William the Conquerer placed many Norman nobles in power in the newly vacated estates. Now, of we look at laws of the time very little actually changes and most Anglo-Saxon laws actually stay on the books. More interestingly, the French laws that are written begin to adopt Anglo-Saxon terminology.

It's important to remember that the French spoken by the Normans was already vaguely Germanic as the Normans a few generations before had been Vikings who had received a land grant of sorts in Normandy to stop their raiding. Their existing Germanic language was usurped on favor of French bit it did in fact leave a mark.

So when the Normans came to power in England they had a mess. Welsh was still actively spoken in Wales and as you went North the languages changed again. So to have a lingua Franca was important. Now this isn't to say the languages were squelched. At this point they weren't. French was the language the laws were written in, but not really. For all important things Latin was still prefered but in all cases Anglo-Saxon words crept in.

Within the court this is the era of ballads minstrels and troubadors begin to arrive. They supliment the traditional Scops the Germanic tradition allowed. But whereas a Scop told stories about the family and its legacy minstrels and bards told for entertainment. To be accessible to the court they had to speak in the secular language and not in Latin. So these stories were related in French. This helped to entice the VERY few remaining Anglo-Saxons to accept French as it became utterly ubiquitous.

In the intervening centuries until the rise of the modern period the primary influence on England was France. Whether they were in battle or in leave England and France just couldn't leave each other alone. So French was necessary. But as local lords began to marry into the nobility and the court stopped seeing itself as Norman but rather English, French became while still the primary language it became not the only language.

They stopped thinking of themselves as French simply because to them they were never French in the first place! They were Vikings who became Normans who became English. And as their holdings in France became less secure it was the ones in England that prospered. Furthermore, the lesser nobles that were still typically Anglo-Saxon began to marry up, and up, and up helping to remove the distinctions between the two. Although it was always known exactly what family you came from as is typical even today amongst nobles. In addition they began to associate themselves with their holdings and not with their allegiance as much. As the court had to take on English responsibilities they began to transition from warriors to landlords. They still fought and what not and don't crucify me for this but they became more concerned with local over foreign. And so they became more English.

As the modern era begins the rise of secular languages explodes the printing press, Chaucer, and everything else contribute and we wind up with language becoming almost nationalistic in a way. Every country wants works of art accessible to them secularly. This leads to people such as Shakespeare who Elizabeth I endorsed. And as the arts became more secular the language of entertainment changed as well. And while most nobles still spoke French the preferred discourse became English.

Now someone could think this is the end but it isn't. French is still the official language of the court today. Most nobles can still speak French as well, but business is conducted in English. This is because technically the house of Windsor is of German descent and during WWII that was a poor association to have. So they changed their agenda to public accessibility (as Prince Philip wanted) and English became finally utterly ubiquitous in use.