How do you know what music (specific titles) is mentioned in Fitzgerald's works or movies or plays based on his works?
There are several ways to discover the titles of the musical pieces mentioned in the works of F. Scott Fitzgerald. A scholar or advanced undergraduate or graduate student working on this topic would read through the complete works of the author underlining references. As Fitzgerald often refers to songs indirectly, by very short excerpts or indirect references, recognizing the specific works to which he is referring would require a substantial knowledge of both classical and jazz music. You can also consult existing scholarship on Fitzgerald and popular music, such as:
Ruth Prigozy (1977). “Poor Butterfly”: F. Scott Fitzgerald and Popular Music. Prospects, 2 , pp 41-67
The musical play, The Beautiful and the Damned, written about the life of Scott and Zelda, has numerous songs including Tender is the Night, I’m Dancing, and So Long.