This is a great question based on this excellent short story. I think to answer it we need to remember the context of what is going on here. Charlie is returning to Paris after a long absence to try and re-claim his daughter from his sister-in-law and her husband, who have been looking after her. Charlie was formerly an alcoholic, and they took his daughter in because he had shown himself unable to look after her. As he returns to Paris, he is constantly thinking about what his life was like then, during the carefree days of ridiculous opulence and wealth, compared to the Paris that he visits now: a much grimmer, bleaker place. Therefore one way in which the past is imposed upon the present is through Charlie's own memories:
He remembered thousand-franc notes given to an orchestra for playing a single number, hundred-franc notes tossed to a doorman for calling a cab.
Another way in which the past literally intrudes on the present is when Charlie meets two "sudden ghosts from the past" in the form of Duncan Schaeffer and Lorraine Quarrles. These former partying friends act as a literal reminder of Charlie's drinking past, and of course their appearance ruin his chances of gaining his daughter.
Finally, the past is brought up by Marion as she tries to establish whether her brother-in-law has reformed and stopped drinking. She reveals to us the rather painful memories of what happened between her sister and Charlie, and we can see her reluctance to believe that he truly has reformed.
The repeated references to the past seem to perform the function of constantly questioning or challenging the supposed sobriety of Charlie. He appears to present himself as a reformed alcoholic, yet at the same time he has a past that he appears unwilling or even unable to escape, just as there are hints that his alcoholism is not completely conquered. Charlie, as he returns to Paris, revists his own personal "Babylon," which is full of ghosts, some of them far more substantial than Lorrainne and Duncan.