They tried to conquer England for the best part of a millennium, failed, conquered parts of France and Italy instead - by war and diplomacy - and then conquered England.
Side note: if that kind of stuff is interesting to you, I can highly recommend The History of English podcast.
You might be able to argue the Normans influenced the normalization towards plurals endings in S, but languages are generally pretty resistant to borrowing grammatic features wholesale versus, say, borrowing vocabulary.
Not always check Spanish for example they took a lot from Arabic, like 'EL'.
Latin did not have articles. The use of articles is a grammatical feature that has been borrowed between languages. But yes: that kind of borrowing is a lot less frequent than borrowing of vocabulary.
Danish, Swedish, and Norwegian have kept more of the insanely complex rules for pluralisation actually.
Danish isn't insanely complex to pluralise (native English speaker who recently learned Danish).
The choice is either add -e or -er with some exceptions.
https://www.duolingo.com/comment/6279406/Plural-Endings-in-D...
Swedish is a bit more complex with arbitrary assigned neutral or uterum gender and definite articles.
But you'd probably be understood using -er in spoken Swedish for a large group of words. Written Swedish is more tricky.
https://medium.com/@mailmyswedish/plurals-in-swedish-76f1de9...
Although they kept the cases - that there are only traces of left in Swedish - even Icelandic seems simpler.
Pretty much same for ox - from the old form of "big" "великий" - big animal.
Cow "корова" most likely comes from protoslavic korva and most likely inherited from ancient-indian "carvati" - "chewing".
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Wamba, up and help me an thou beest a man; take a turn round the back o' the hill to gain the wind on them; and when thous't got the weather-gage, thou mayst drive them before thee as gently as so many innocent lambs."
"Truly," said Wamba, without stirring from the spot, "I have consulted my legs upon this matter, and they are altogether of opinion, that to carry my gay garments through these sloughs, would be an act of unfriendship to my sovereign person and royal wardrobe; wherefore, Gurth, I advise thee to call off Fangs, and leave the herd to their destiny, which, whether they meet with bands of travelling soldiers, or of outlaws, or of wandering pilgrims, can be little else than to be converted into Normans before morning, to thy no small ease and comfort."
"The swine turned Normans to my comfort!" quoth Gurth; "expound that to me, Wamba, for my brain is too dull, and my mind too vexed, to read riddles."
"Why, how call you those grunting brutes running about on their four legs?" demanded Wamba.
"Swine, fool, swine," said the herd, "every fool knows that."
"And swine is good Saxon," said the Jester; "but how call you the sow when she is flayed, and drawn, and quartered, and hung up by the heels, like a traitor?"
"Pork," answered the swine-herd.
"I am very glad every fool knows that too," said Wamba, "and pork, I think, is good Norman-French; and so when the brute lives, and is in the charge of a Saxon slave, she goes by her Saxon name; but becomes a Norman, and is called pork, when she is carried to the Castle-hall to feast among the nobles; what dost thou think of this, friend Gurth, ha?"
"It is but too true doctrine, friend Wamba, however it got into thy fool's pate."
"Nay, I can tell you more," said Wamba, in the same tone; there is old Alderman Ox continues to hold his Saxon epithet, while he is under the charge of serfs and bondsmen such as thou, but becomes Beef, a fiery French gallant, when he arrives before the worshipful jaws that are destined to consume him. Mynheer Calf, too, becomes Monsieur de Veau in the like manner; he is Saxon when he requires tendance, and takes a Norman name when he becomes matter of enjoyment."
"By St Dunstan," answered Gurth, "thou speakest but sad truths; little is left to us but the air we breathe, and that appears to have been reserved with much hesitation, solely for the purpose of enabling us to endure the tasks they lay upon our shoulders. The finest and the fattest is for their board; the loveliest is for their couch; the best and bravest supply their foreign masters with soldiers, and whiten distant lands with their bones, leaving few here who have either will or the power to protect the unfortunate Saxon. God's blessing on our master Cedric, he hath done the work of a man in standing in the gap; but Reginald Front-de-Boeuf is coming down to this country in person, and we shall soon see how little Cedric's trouble will avail him. ---Here, here," he exclaimed again, raising his voice, "So ho! so ho! well done, Fangs! thou hast them all before thee now, and bring'st them on bravely, lad."
The -s endings came after Norsemen conquered England, and the introduction of it was from their language, connected to old French. This also is why in English, you have words like "ox/cows" and "beef": the Norsemen who were nobles essentially influenced the English to use their words for the animals since they were served as food to them (beef), while the English people who slaved in the fields raising the actual animals (cow) continued to use their ancestors' words for the live animals. This is why we have different words for the meat of the animals (beef, poultry, mutton) vs. the actual animals (cows, chicken, sheep).