Could a language change so much that it becomes part of another language family?
You are born in a certain place and have specific parents. Who your parents are never changes no matter what you do or where you go in life. You could have been born in Australia and move to northern Scandanavia and your parents will still be who they are.
It is like this with languages. English is a Germanic language because it is descended from a language spoken by Germanic tribes. It has taken on many Romance language derived vocabulary, but that doesn’t make it a Romance language anymore than moving to Scandanavia makes you a Scandanavian.
But if you were to have a child in Scandanavia, it would be fair to call your child at least partly Scandanavian. Language is not one thing but changes over time. There is no single point at which Old English became Middle English. It changed gradually. Let’s imagine a language starting in Australia and being brought for some reason to Scandanavia (just to continue the analogy). It would still be regarded as having been born in Australia, but after some time it would be regarded as a Scandanavian language.
Could English change language families? No. But a language spoken in England that took influences from English and French and other languages could be regarded as a Romance language if history were different. And if such a language existed, it would be fair in this alternate worl to call it English.
What would have happened if the English that we know had died out? Imagine an alternate scenario where not only did the Anglo Saxons lose in 1066, but the Normans managed to hold onto their land in England and Normandy.
The beginning of the end of the dominance of French in England was the defeat of Normandy to France. This cut off the Normans in England from Normandy and they eventually assimilated into English society. Over the next decades and centuries English would reemerge, changed, but not forgotten.
What if this hadn’t happened? French would have continued its dominance in England, and English as we know it would have slowly died out. English would be replaced with French, but the French spoken in England would be slightly different to the French spoken in France.
Maybe the French in France would look down on what they called “The bastardised mutterings of those English fools” or something to that effect. They would think of the French spoken in England as bad French, as not the real French. Maybe eventually the English themselves would get tired of this attitude and assert themselves with the attitude that actually the way they spoke was perfectly alright and it was merely the stuck up French who had a problem.
Maybe the English would fight the French for independence and win and to secure their victory they would say to the world, “We are English and we speak English”. But remember, in this alternate scenario, the English we know is gone. So what do we call this Anglo-French spoken in England? Why not just call it English.
This language would probably have a lot of Germanic-English loan words and would probably be pronounced a bit differently or maybe very differently to the French spoken in France. But going back to the original question, it would not be classed as a Germanic language. It would be classed as a Romance language because it descended from French.
This is how a word like “English” could go from refering to a Germanic language to refering to a Romance language. Could a language change families? No, but something connected or associated with it might have a very different story than languages spoken before it.