It's a non-animated movie about a boy who was born old, but grew young and dies as a baby.
He fell in love, but the girl grew old normally and dies, while this guy grows younger and finally dies as a newborn.
This is The Curious Case of Benjamin Button.
The film stars Brad Pitt as a man who ages in reverse and Cate Blanchett as the love interest throughout his life.
As pointed out by @Edlothiad in the comments (but him being "very content with it as a comment"), this is The Curious Case of Benjamin Button (2008), based on a 1922 short story of the same name. OP has apparently indicated that was it in another comment.
Benjamin Button, a baby that was born looking like an old man, is taken in by a nurse at an old folks home. Over the years as Benjamin got "older" he appeared to get younger. As he lives at the home, he meets Daisy, a beautiful young girl the same age. He falls in love with her, knowing the relationship will always look strange. Will his disability get in the way of true love? Or will it set him free?