But poetic realism is one of those terms that are both specific and vague, and where it seems each person who use it defines it slightly different. Sometimes the term is used so broadly it becomes another way of saying "French films from the 1930s" and sometimes it is just about only the handful of films written by Jacques Prévert in the 1930s and early 1940s that are included, most of which were directed by Marcel Carné. This is unsatisfying because if we want to use a term it should mean something concrete, otherwise it becomes meaningless. And for it to mean something concrete it is not enough to define it, your examples of it must also fit that definition. When you use it to include everything from La Kermesse héroïque / Carnival in Flanders (Jacques Feyder 1935) to Pépé le Moko (Julien Duvivier 1937) to Port of Shadows (Marcel Carné 1938) to The Rules of the Game (Jean Renoir 1939) it has no meaning as those films have nothing in common (whether style, tone or settings or themes) other than being French films of the 1930s. You can of course call them all examples of poetic realism if you wish but then your definition of poetic realism needs to be able to include such disparate art works. If the definition cannot do that, do not call them all examples of it.
Port of Shadows
While poetic realism is the term overwhelmingly in use today, others have been used before to talk about some of the same films, such as "populist melodrama" or "fantastique social" and that is relevant as it shows how ill-defined the concept is. Many critics and historians (including Ginette Vincendeau and Rémi Fourier Lanzoni) argue that central to poetic realism is a depiction of the lives of the working class, but while it is true that Jean Gabin's character in Daybreak / Le jour se lève (Marcel Carné 1939) works in a factory, I would not say that the films most commonly included under the banner of poetic realism (such as the four above) are on average about the working class in any particular way. An urban setting, particularly Paris, is also often considered a key aspect but this is by no means generally true. Many of the films that are frequently referenced as poetic realism are set in rural areas or in French colonies. I would not include La Kermesse héroïque among poetic realism but many do, even though it is set in 17th century Flanders.
One problem in the discussion is that during the 1930s over hundreds of films where made each year in France (some years up to 160 films were made), and the ones that are being discussed are such a very small portion of that. This small sample pack might give the appearance that poetic realism was a prevalent style but that is probably not true at all. Although until you have seen the roughly 1200 films made during the decade, you cannot say how many that can reasonably be called poetic realism.
But while there is a lot of confusion and incoherence, there is something we could refer to as poetic realism, but it should be used with more specificity, and your examples should fit your definition. That Port of Shadows is a prime example of poetic realism seems uncontested, one of the few films that everybody agrees upon. What it has is a sense of melancholia and fatalism, of people hiding out from the world as existential fugitives with a troubled past and no real hope of a tomorrow. It is shot with a beautiful combination of sets and the real world and in a black and white that is leaning towards grey, and with an infrequent mist adding texture. The narrative is often loose, and the focus is on the characters and their interactions rather than the story at large. A film must not have all of these features to qualify, some aspect might be missing, but it should be close enough, an outlook on life and a particular view of character. This to me is poetic realism. My definition is perhaps too narrow for some tastes but I think it must be if it is to be meaningful. Even if it is not an exact science, it should still be coherent. At the same time I do not think it is unique for France, as is almost always said. We can talk of it as a more global trend.
In Mists of Regret (1995), Dudley Andrew's rich book about poetic realism, he suggests Griffith's Broken Blossoms (1919) as an early example of poetic realism or, as he puts it, "arguably the first major film explicitly intoning the poetic realist appeal." (p. 36) But that is an outlier, and Andrew does not pursue an American poetic realism (see my first footnote). One could instead consider some films of Josef von Sternberg, from the late 1920s and early 1930s (such as Morocco (1930)), as other contenders. Frank Borzage's adaptation of A Farewell to Arms, made in 1932, comes close to adhering to my definition, as do Allan Dwan's While Paris Sleeps (1932). And then there is Howard Hawks.
In 1939, the same year as Carné made Daybreak, Hawks made Only Angels Have Wings. It has all the traits and attributes of poetic realism, the men and women huddled together away from the world at large, living in the moment since the past is best to be forgotten and the future is bleak. The narrative has a meandering quality and despite a story filled with drama and tension, it is leisurely told with primary attention given to character interactions and relationships. Visually, Only Angels Have Wings is also within a style of poetic realism, both cinematography and set design.
Only Angels Have Wings
There are other films by Hawks that can be discussed as poetic realism, such as The Road to Glory (1936) that was inspired by the French film Les Croix de bois (Raymond Bernard 1931). The last example of Hawksian poetic realism is To Have and Have Not (1944). Like with Only Angels Have Wings, it is easy to imagine that Jean Gabin's character Jean from Port of Shadows will just walk in one day and join the group.
Both Only Angels Have Wings and To Have and Have Not were co-written by Jules Furthman, who also participated on the scripts of some other films by Hawks and some early films by Josef von Sternberg. Furthman is undoubtedly an important figure within American poetic realism.
My argument is not that Hawks was explicitly influenced by the French, the argument is that the style and mood was more universal than French. In the 1940s Swedish filmmakers like Hasse Ekman and Ingmar Bergman were clearly influenced by certain aspects of French 1930s cinema, but that is something different. The usual argument is that French cinema of the 1930s was an antidote or an alternative to Hollywood, but that is a monolithic view. With thousands of films made in each country, the output is too rich and varied for such neat dichotomies. When you compare one specific masterpiece like Stormy Waters / Remorques (Jean Grémillon 1941) with a generic, unspecified Hollywood production then of course the French film will be different and superior. If you compare one Hollywood masterpiece, such as Holiday (George Cukor 1938), against a generic, unspecified French film it will be the Hollywood masterpiece that is different and superior. But either comparison is weak and will not tell you anything of value.
Another argument I make is that it is wrong to treat all Hollywood films as following the same narrative structure, in contrast with other countries. There are plenty of variations of narrative within classical Hollywood, as I have argued elsewhere. Hawks is an example of that, and looking at it from the perspective of poetic realism can yield interesting insights.
The Road to Glory
Despite his claim for Broken Blossoms, I do not think Dudley Andrew would agree with these American examples. A large part of the introduction to Mists of Regret is focused on "proving" that Hôtel du Nord (Marcel Carné 1938) is by default better than anything made in the US in the 1930s. A peculiar argument to make about a decade that saw Ernst Lubitsch, John Ford, Howard Hawks, Frank Borzage, George Cukor, Henry King, Henry Hathaway, John M. Stahl and others do wonderful things. Andrew's book is beautifully written but it has its faults.
Besides directors, perhaps the most important contributors to French cinema of the 1930s were the art directors and set designers, like Alexandre Trauner and Jacques Krauss. Another one was Lazare Meerson. He was indisputably a master, as can, for example, be seen in his work for Feyder and René Clair. But by the time poetic realism really got going Meerson had moved to Britain (in 1935) and he died suddenly in 1938 from meningitis. On his last film, The Citadel (King Vidor 1938), Meerson was replaced after his death by Alfred Junge, who would later be a key collaborator with Michael Powell and Emeric Pressburger. Had Meerson not died so young he might have been that key collaborator instead.
Here is something I wrote about Spawn of the North (1938), a film directed by Hathaway and written by Jules Furthman: https://fredrikonfilm.blogspot.com/2012/06/spawn-of-north-henry-hathaway-1938.html
I discuss different kinds of narratives in Hollywood cinema in my chapter in the book ReFocus: The Films of Budd Boetticher (2017).
A Farewell to Arms