You are thinking of:
the American pianist and composer, George Gershwin (1898-1937).
This can be worked out by noting that many of the lines clue the titles of some of his most famous works, all of which can be found on the album Gershwin Plays Gershwin: The Piano Rolls, a compilation released in 1993. In fact, the title is a big reference to one of his most famous pieces of all, Rhapsody in Blue, which is also on the compilation album.
Uncle Sam took a journey to France,
An American in Paris
Sky-high wisps for to move with his feet,
Kickin' the Clouds Away
And to feel a particular emotion,
That Certain Feeling
A feeling so down-low and sweet.
Sweet and Lowdown
He'd have liked to go buy up his favorite,
But, alas, there were none in the stack.
There was someone who did get to buy it,
But disliked it, and gave it right back.
This whole paragraph is a reference to When You Want 'Em You Can't Get 'Em, When You've Got 'Em, You Don't Want 'Em
He cut a short story in quarters,
Novelette in Fourths
Then daydreamed of young golden cows,
Idle Dreams - since 'idle' sounds like 'idol', with a reference to the 'golden calf' from the Biblical account in Exodus.
But that night, he was up without slumber,
Thinking thoughts while he furrowed his brows.
On My Mind the Whole Night Long. This might also feasibly reference Sleepless Night - an unpublished work listed on this Wikipedia page.
