The conflict in "Babylon Revisited" would seem to be between the protagonist, Charlie—who wants to regain custody of his daughter, Honoria—and his sister-in-law, Marion, who doesn't trust him. But really the conflict is between Charlie and his past, which is represented in the story by his friends Lorraine and Duncan and also by Paris itself, which was the scene of Charlie's dissipation and alcoholism in the 20s. It was also the scene of the incident that led to the death of his wife, Helen. By returning to Paris, Charlie is trying, in effect, to erase the past.

One way to think about the story's connection to modernist ideals is to think about Charlie's reinvention of himself, as a businessman and a responsible father, as a kind of progress. Charlie's embrace of middle-class values and work ethic can be seen as a kind of corrective measure, a way to make himself "new," but it's clear that Marion is right to be suspicious of him: his decision to only take one drink a day is meant to be a show of willpower, but it can also be seen as an unwillingness to truly let go of the days when he was rich and idle.

Fitzgerald wrote Babylon Revisited in 1930, a time in between  the two World Wars and the Great Depression, but just after a period of economic prosperity and decadence known as the Roaring Twenties, a period that profited Charlie Wales, the protagonist and his wife Helen.  

Charlie's internal conflict is defined by his grief and guilt over the loss of his wife, who died as a result of getting a terrible chill from walking to her sister's apartment when Charlie locked her out because he was angry at her.  He feels responsible for Helen's death which is attributed to a failed heart.  He is also battling his own disease, alcoholism. 

His external conflicts are with Marion Peters his sister-in-law, who has legal custody of Honoria, his daughter, and his old friends in Paris, like Lorraine Quarreles.

Charlie has returned to Paris to get his daughter back from Marion, but she is not easily convinced that he is in the right circumstances either physically, emotionally or financially to take care of Honoria. Charlie tries to convince Marion that he is ready.

".... I  worked hard for ten years, you know—until I got lucky in the market, like so many people. Terribly lucky. It didn't seem any use working any more, so I quit. It won't happen again." In Marion's mind, Charlie's responsibility for Helen's death is inseparable from his financial success: he should feel guilt for both.