This is a modern musical based on classic French films, like The Umbrellas of Cherbourg (1964) and old American Gene Kelly pictures. That old-Hollywood and classic film aesthetic bleeds into the production of the film, down to the technicolor cinematography, the wardrobes, and Gosling's watch.
He wears a small, and seemingly gold, 34mm Omega with applied 12, three, six, and nine markers on a leather strap. I've written about old Omega watches from the 1940s and '50s in the past, and one thing I know about those watches is that they were plentiful. Many confuse these for early Seamasters (also plentiful in those days), but in fact, Gosling's watch is a simple Omega logo-only and time-only piece. Obviously, without seeing it in person, it's impossible to deduce exactly what this vintage piece is. That being said, there is enough by way of the overall aesthetic elements to make me comfortable in identifying it as something in the universe of a mid-century Omega "Trésor."
Example of an early 1950s Omega Trésor from the Omega archives. This watch has the "Automatic" designation and a small seconds indicator, whereas the La La Land watch has central seconds and "Omega"-only text.
La La Land is about the fraught love story between Mia and Sebastian. And every love story has a first date. In their case, a showing of Rebel Without a Cause (1955). It's in this scene that Sebastian wears his blazer and vintage slacks get-up. Mia is late arriving at the theater, and Seb sits anxiously in his seat, checking his Omega watch for the time. Eventually, she does arrive in a dramatic fashion. The two enjoy the film and then prepare for a kiss. That's when the film stock burns and the lights come on in the theater. Show's over folks. Just as this happens [00:54:47], Seb puts his hand to his face, revealing the little Omega on his right wrist. 041b061a72