What is the significance of the appearance of the wolf?

Director Wes Anderson said of the scene:

There were some people who didn’t like the wolf scene. In particular
one very important person. And he said, I don’t understand what this
scene is doing in the movie. And I would always say to him, I’m not
cutting it. That scene is why I’m making the movie.

So what does it mean?

Actor Jason Schwartzman, who plays a 12-year-old fox in the film, said:

...we stop and we see a wolf on a distant hill, and it’s a really
beautiful, beautiful scene. It’s like so heart-warming because it’s
just a beautiful moment between these foxes and little animals and
this really like mysterious wolf who we’ve heard about the entire
movie and who doesn’t talk in this scene and he’s not wearing clothes.
He’s kind of, he represents I guess, the wild. He’s a wild wolf and
animal, and it’s a beautiful moment where they have this great
connection, and in that moment, it really like to me the point of that
scene is let’s keep on being free. Let’s keep on being animals. And
it’s such an uplifting moment, and like when I’ve seen it with
audiences, a bunch of people break into huge cheers and hooting. It’s
such an awesome, awesome scene. It really just blows my mind.

An anonymous reviewer stated this more eloquently:

I think it shows that Mr Fox is afraid of his wild side and yet
desires greatly to live it due to fears that he has become
domesticated. The wolf represents pure, unbridled, rugged and wild
power. Mr Fox tries to communicate with it but realises that being
wild is not for him and is best left to the wolf. He exchanges a
symbol of brotherhood with the wolf and returns to his family and
community while the wolf returns to its harsh forest, not needing a
thing in the world, being truly free.

And finally, this article by Shana Mlawski talks about the scene in the context of the plot, suggesting that the movie is about castration. Mr. Fox has had his tail shot off and he is trying to get it back, at the same time that he is trying to revert to his wild nature from the domesticated life he had taken on in in order to support his family. An excerpt:

The ambiguity of Mr. Fox’s decision to give into his natural, wild
impulses can also be seen in his relationship with the Wolf.
Throughout the film, Mr. Fox shows that he is afraid of the Wolf.
“Wolf? Where?!” Fox says, cowering with eyes wide open. The Wolf is
described as the wildest, most frightening, and yet most beautiful
creature in the world. Mr. Fox fears the Wolf and yet wants to be
exactly like him. We can thus say that Mr. Fox fears pure, wild
masculinity yet also yearns to own it himself.

After Mr. Fox and Ash save Kristofferson and Mr. Fox’s ruined tail,
Mr. Fox actually does meet the Wolf, his masculine ideal.
Significantly, Mr. Fox cannot speak with him. The Wolf, being the
representation of pure wildness, cannot speak English (or French, or
even Latin—which is important, because it means that Wolf cannot even
understand his own “scientific” or “natural” name, which is of course
as culturally-determined as the names “Wolf” and “Mr. Fox”). Mr. Fox
does pump his fist at the Wolf to say, “Fight the Man,” but that is
all Fox can do. His wife is pregnant again; he cannot live in the
wild world of the manly wolves. He can only learn to survive his
neutered life in the suburbs.

The review continues on, assessing the moral of the story – a very interesting read about the male midlife crisis.