This question actually brings together two interesting historical narratives, one about the evolution of migration restrictions and the second about the particular status of interwar Paris.

To answer the first: there’s a few pieces of context that are important for framing this question. First, there’s a difference between passports and emigration quotas or visas. Some scholars would argue they come from the same impulse to surveille and control population movement, but functionally, countries tend to track entries and exits for decades before they start doing anything about it. Second, migration policy has generally not been developed comprehensively or systematically. Instead, countries tend to pass migration restrictions in very piecemeal ways, targeting very specific groups, in reaction to specific events. For example, historians generally identify the Chinese Exclusion Act of 1882 as the first major migration policy in the U.S., which, as the name suggests, targeted Chinese migrants to the west coast of the U.S. This was the culmination of a series of policies that sought to restrict Chinese emigration in response to anti-Asian sentiments among miners and workers in California. But this act didn’t prompt a broader assessment of migration policy, or a comprehensive system of controlling migration- the first “quota style” law in the U.S. wasn’t implemented until the Emergency Quota Law of 1921. (Ngai, Impossible Subjects, 2014) The main point here is that countries don’t suddenly implement comprehensive immigration policy; instead, these have grown more and more restrictive over the twentieth century. This is also the case in France: discussions of passport control and limiting movement occurred as early as the French Revolution, but these policies were never fully implemented; and movement in and out of the country was generally unregulated through the 19th century. WWI provides the impetus for more stringent controls, and France started requiring resident foreigners to carry specific documents; but did not develop broad policy about entry or exit. In fact, persistent labor shortages in France through the 1950s meant the French economy relied on immigrants for several decades. The first restrictions occurred in the 1970s, in response to an economic downturn, and were directed against former colonies. (Torpey, Invention of the Passport, 2000)

If that’s the broad context for how migration regimes form, there’s also some specific context about interwar period and Paris that’s important to this question. First, the interwar period in Europe was a moment when concepts of nationalism as well as actual nations were in flux. WWI ended with the dismantlement of Europe’s remaining land empires (Austria, Russia, Germany, Ottoman) and the creation of new “nation states.” These shifts produced significant population movement, and made it functionally difficult to insist on travel or identification documents. What to do about migration is a subject of political debate in the newly formed League of Nations, with some pushing for greater freedom of movement and others asserting nations rights to control their borders. So, intellectually and legally, the concept of migration restrictions are under debate; and functionally, the French government doesn’t have bandwidth to administrate a comprehensive visa system. (Torpey) For context, an estimated 3 million immigrants, or 6 percent of the population of France entered in the interwar.

Paris itself is very central to these shifts as the site of the Paris Peace Conference (1919-20). In addition to bringing official representatives from the victorious nations, discussions of national-self determination attracts colonial representatives who see this as their moment to make arguments for their own independence. Paris also has a significant number of former soldiers, especially from colonial regiments, who decide to stay after peace is declared. So in the 1920s, Paris was becoming an international center of political and intellectual discussion about nationalism and the postwar order. This large international presence also leads to a dynamic social and artistic scene. All this is facilitated in part by France’s still unsettled migration policy, which functionally means if you can get there, you can stay. (Goebel, Anti-Imperial Metropolis, 2015) So in coming to Paris, Stein, Baker, Hemingway, and other Americans are part of a larger movement towards Paris, as Paris becomes an international center of intellectual and artistic life. Paris’ republican identity and socially liberal reputation also makes it particularly attractive to both anti-colonial and civil rights figures.

So in short, in the interwar period, French migration policy was in flux and American visitors would not have necessarily stood out within a very international city.