Here's a new vocabulary word for you: droll. As in, "Adam Cook is one seriously droll dude." The wordsmiths at Merriam-Webster define droll as "having an odd and amusing quality." We'd say that sums up Adam Cook, wouldn't you? He's dry, self-deprecating, and, at first glance, it's not entirely clear why he's in the movie in the first place.
The Artists Who Starve Together…
On closer inspection, it's clear that Adam serves several purposes in An American in Paris. First, he's Jerry's neighbor, his sounding board, and, arguably, his best bud in Paris. He's also a fellow starving artist, although Adam's medium is the piano, and boy can he play. But more on that in a moment.
Just like Jerry, Adam knows the creative struggle is real, and he's got a witty quip for every occasion, like when Jerry asks to borrow a few francs for lunch:
JERRY: Hey, Adam, you wouldn't have 300 francs on you, would you? I'm going to Montmartre, and I need lunch money.
ADAM: Sorry, kid. Bought a postage stamp this morning, and it broke me.
Adam may not always be able lend Jerry some cash, but he's always down to lend him his ear, especially when it comes to women. Whether it's his spot-on suspicions about Milo's true intentions or the emotional roller coaster ride that is Lise, Adam has Jerry's back.
When Jerry's flying high after a meeting with Lise, Adam accompanies him on the piano through an ebullient rendition of "Tra-La-La (This Time It's Really Love)." When Jerry's down in the dumps because Lise has ditched him (again), Adam listens to his pal's girl problems, even though it's pretty clear from his interactions with equally Lise-crazy Henri that Adam's never experienced those problems himself:
HENRI: So be happy! You only find the right woman once.
ADAM: That many times?
Adam applies this same level of self-deprecation to his music career. He lacks drive just as much as Jerry does, but unlike Jerry, Adam shows self-awareness. He knows that if he wants to call himself a concert pianist, he actually has to, you know, play some concerts:
ADAM: I'm a concert pianist. That's a pretentious way of saying I'm unemployed at the moment.
Similarly, he knows that the biggest obstacle on his road to piano stardom is himself:
HENRI: What are you working on?
ADAM: Same old concert.
HENRI: When are you going to give it?
ADAM: When I can't figure out any more reasons not to.
While Jerry's in denial about his skills—or lack thereof—as an artist, Adam knows he's got the goods. He just isn't in any hurry to show them off and risk failure.
Adam also plays a crucial role in the film's plot. He's the link between Jerry and Henri, whom he sometimes accompanies on the piano. It's Adam's friendship with both lovesick gents that lets the audience in on the love triangle at the center of An American in Paris.
Of course, at first, Adam doesn't know that his two pals are gaga over the same gal. When he puts it together, though, he deals with it in exactly the manner you'd expect from a mordant, chain-smoking artist—he silently freaks out, guzzling brandy and lighting cigarette after cigarette.
George and Ira and Adam and Oscar
Adam isn't just the link between Jerry and Henri, though. He's also the link between An American in Paris and the music of George and Ira Gershwin. Or rather, Oscar Levant, the famously acerbic comedian and real-life piano prodigy who plays Adam, is the link. All of the musical numbers in An American in Paris are Gershwin tunes, and off-screen, Levant was one of George Gershwin's BFFs. Not only that, but most critics agree that Levant is one of the best interpreters of the Gershwin catalog, and that's a mighty big catalog (source).
In other words, if MGM were going to build a movie around the songs of George and Ira Gershwin, then Oscar Levant—with his trusty piano and drier-than-the-Sahara wit—needed to be in it. He keeps the story, and its music, humming.