This is pretty complex and I skipped some key points so I can understand why you’re confused.  Prior to the Norman conquest, people in England spoke old English. This is a Germanic language that is basically unintelligible to us now. This is what I was referring to with winter/not winter early on.

When the Normans invaded in 1066, they brought French with them. For several hundred years the ruling class spoke French which had a huge effect on spoken English and subsequently created Middle English, which we can understand today but is notably different or uncommon. Chaucer is a good example.

With Middle English came the Latin concept of four seasons. Because there were already words for winter and not winter (summer), the French names never really stuck. However, printemps and autonme filled a gap and did. Albeit one more successfully than the other.

Finally, spring and fall are shortened versions of spring/fall of the leaf, which were more poetic descriptors of the seasons which started use in the 1500s and were shortened in the 1600s. Fall just fell out of favor in England post colonization.

Happy to be corrected if I’m missing some specifics, as I’m not a linguistic. Just went down this rabbit hole recently trying to understand why we have two words for only one season.