This story is written in the third person, but whether the narrator is omniscient or limited is debatable—omniscient means that the narrator has access to the internal perspective of multiple characters, while limited means that they only have access to the internal thoughts and feelings of a single character at a time. When the narrator tells us how Marion feels about Charlie—that she hasn't forgiven him for the way he behaved in the past—it is possible that we are getting this information from Charlie's impressions of her. Certainly you can imagine Charlie thinking to himself that Marion felt it necessary to "believe in tangible villainy and a tangible villain."

When considering a narrative "point of view," we don't just look at these factors, though. As close readers we also need to think about the narrator as a character in and of themself: how do they treat the characters? Are they sympathetic or do they judge harshly? What can we say about the narrator as a character in the story? And do we trust that they are giving us the full story? How does the narrator want us, the reader, to feel about the story? Everything the narrator tells us, and the way they tell us, is a deliberate choice.

With this in mind, let's have a closer look for some clues about these questions within the story.

An example of the narrator giving us extra information that isn't strictly necessary is when Alix tells Charlie that Claude is in Paris, but that he isn't allowed into the Ritz. The narrator begins the paragraph with, "Alix lowered his voice confidentially: 'He's in Paris, but he doesn't come here anymore.'" There are a couple of choices that the narrator has made in the way they've told us what Alix says. Firstly, they've put the speech marker at the start of the sentence: they want us to know how Alix spoke before we hear what he said. So the narrator has foregrounded the fact that Alix lowered his voice.

In addition to this, the narrator hasn't just told us that Alix lowered his voice, they've told us that he did it "confidentially." By doing this, the narrator has given us extra information to understand what is happening: the way the character speaks is important to the mood of the words that follow. Consider the difference to the mood of this section if the narrator hadn't told us how Alix spoke. By choosing to show us these extra details, the narrator has shown us that their perspective is somewhat conspiratorial or gossipy: they are actively making a judgement of the characters.

As no character is telling the story him/herself, this is 3rd person point of view.  Fitzgerald cheats a little, though.  A story in 3rd person should either be limited - through the eyes of a single character - or omniscient - through the eyes of multiple characters.  Fitzgerald does both.

He mainly uses limited, gearing the narrative through Charlie's perspective.  Everything that happens is portrayed as Charlie sees it, allowing the audience to both be removed from Charlie, but exposed to his "vision".  Since the conflict is Charlie's and is very personal (dealing with grief), this choice of point of view makes sense.  Here is an example:

• "He would come back some day; they couldn't make him pay forever. But he wanted his child, and nothing was much good now, beside that fact.... He was absolutely sure Helen wouldn't have wanted him to be so alone."

In the above passage, it is Charlie's hopes and plans that the audience hears.  In contrast, here is an example of Fitzgerald breaking the rules and letting in another character's perspective:

• "...part of her [Marion] saw that Charlie's feet were planted on the earth now, and her own maternal feeling recognized the naturalness of his desire;"

This occasional break from the technique allows readers momentary glimpses into how Charlie is viewed by others, broadening our understanding of the protagonist.