That was likely a big part of it. Although other factors are things like the 100 years war. Where some of it was about the English Crown also being the "rightful" crown of France, and holding a French speaking court would help in that.
No, the English Crown never had the right to the French crown; they claimed rights to land in France. The French argument (which you will hear at Bayeux) is that Harold Godwinson and his predecessor were vassals to Duke William of Normandy. Harold got a bit above himself and refused to honour William so William took him down a step. By agreement with the French king William held sway over huge areas of what is now France from the channel down to the Pyrenees. In those days with the huge distances and the difficulties in travel the King appointed Consuls to administer the areas of France and they had virtually plenipotentiary rights. From time to time they did rebel and were put down by the king and, on one occasion, the Duke of Leicester. Over the years those areas threw off the control of William's successors.
My knowledge of English history is abysmal; the 100 years war the French talk about was with Spain and was eventually the subject of a treaty which required the marriage between the Infante and the French king at St Jean de Luz.
On top of that they did not speak French as we know it; "French" was created in the 1600s (but became effective in the 1800s) by amalgamating the patois of just four areas, all in the area of the Ile de France (ie Paris). Everywhere had (and still has) its own patois with, I think, four groupings - Breton, still used in that area, oïl,µµ (Latin derivatives) in what is now the northern half of France and Occitan (very different Latin derivatives closer to Spanish) in the southern half of France, parts of Italy and of Spain and Basque - an ancient tongue unconnected with any other language.
µµ One of the patois, Jerrois, is still used in Jersey - I can just about understand written it but it is very different to modern-day French
"If you only speak English(or local dialect thereof), you must be a peasant, as any person of means would at least bother to learn French."
By 1076 95% of Britain was under the control of the Normans and the Saxons were reduced to the role of vassals or effectively slaves. They wouldn't get any education whilst their masters still spoke their old language.
One thing puzzles me and perhaps someone here knows the answer. William and his followers were Vikings from Denmark and southern Sweden; in the two hundred or so years they were in Normandy why did they give up their original language?