Well, I suppose this question depends very much on who you side with when you think about the characters in this short story. The protagonist is the character who is trying to achieve something and the antagonist is the character who is trying to stop them. If you side most with Nathalie, you would therefore say that she is the protagonist and the antagonist, the person who is stopping her from achieving her dreams and goal, is actually the rather foolish and ignorant Brantain who sees her with Harry and then threatens to break off their relationship.

However, if you see things the other way round, you could argue that the rather naive Brantain is the protagonist and that Nathalie is the antagonist. She is clearly a calculating individual who has no love for Brantain at all and only wants the wealth and prestige that marriage to him would give her:

The rather insignificant and unattractive Brantain was enormously rich; and she liked and required the entourage which wealth could give her.

If we take this view of the story, then Brantain is the poor man who cannot be saved from the rather sinister designs placed on him by Nathalie, and Brantain is therefore the protagonist with Nathalie being his beautiful nemesis.