Why is Christmas sometimes referred to as Noël, particularly in old Christmas carols? It comes from the Latin natalis, meaning birth, as part of the phrase Dies Natalis, meaning birthday. One of the most common ways the phrase was used in Ancient Rome was to refer to Dies Natalis Solis Invicti, the birthday of the Roman sun god Sol Invictus, which, in an amazing coincidence, took place on Christmas Day.
The name Noel (and of course the feminine Noelle) also comes from this meaning, and this is true for the name as translated into other languages. I was always struck, for example by the versatility of the Irish-language name Nollaig, which means, Noel, Noelle, December, and Christmas.
So if you have any version of the word Noël, I hope you appreciate it at this time of year!