Maine Coon cats are big fur balls and if you get one it will own you, you'll become its staff.
All cats are territorial.
I have a 20 pound cat, however it isn't a Maine Coon cat. He bosses me around and if I don't go where he wants me to or do what he wants me to he'll nip my ankles.
No one enters his domain without his approval, just like a roo watching over his flock. He just looked at the chicks when they first arrived and then walked away. I would not expect a cat to keep a fox at bay, especially a vixen with kits. We had a grey fox vixen with kits early this past summer, she was quite perturbed about my wife getting between her and the kits. My wife didn't even notice momma and got between them, I had to yell to get my wife to back out of the situation.
We also have hawks, eagles, falcons, fishers, raccoons, skunks, coyotes, weasels, and other assorted critters to go with our fox population.
If you can't kill them and want to keep chickens then you need a fort Knox coop and run.
Personally the biggest external threat to our chickens has been the dog next door.