J.K. Rowling, the author of the Harry Potter series of books does not specify what sort of cat Mrs Norris is in terms of cat breed except to say that she is “just an intelligent (and unpleasant) cat”.
The film makers who turned the books into films decided to use three Maine Coon cats to play Mrs Norris. Their names are Maximus, Alanis and Cornilusa.
The films were made in the UK. Therefore the Maine Coon cats employed would have been bred by a British Maine Coon breeder almost certainly.
Often UK Maine Coon breeders get their foundation cats from America because America is the home of the Maine Coon. The breed is essentially America’s great domestic cat. America and the Maine Coon go together like apple pie and custard.
It is ironic that a quintessentially English film includes a quintessentially American cat.
They probably chose the Maine Coon because it is the largest cat breed and a distinguished looking cat. Although the cat in the picture (a screenshot from one of the films) shows Mrs Norris not looking very distinctively Maine Coon. I have seen Maine Coons who are better bred. Indeed this Maine Coon does look like a British bred cat. The British Maine Coons are less ‘type’ meaning less compliant to the America cat association breed standards.
The Russians bred the most outstanding Maine Coons. They are awesome. The have exaggerated Maine Coon features; very square muzzles, enormous ears and human faces.
Mrs Norris is Argus Filch’s sidekick. Filch is Hogwarts’ caretaker. Mrs Norris ‘acts as a hallway monitor or spy for Filch. If she observes students engaging in suspicious activity or out of bed after curfew she finds Filch and he arrives in seconds’ – Wikipedia.
What sort of cat is Mrs Norris? She is a brown tabby domestic cat who happens to be a Maine Coon purebred cat but JK Rowling did not specify that Maine Coons or any other purebred should be used in her books unless she discussed it at the filming stage and approved the use of this breed.
P.S. Someone asked whether Mrs Norris is a ‘Maledictus’. This is a ‘a female individual who carries a blood curse that eventually turns her into a beast permanently’. I think the answer is No. But I will happily be corrected in a comment.