Chapter 6 of the book "Transnational Soldiers.
Foreign Military Enlistment in the Modern Era" (the chapter can be found here, although paywalled) deals with recruitment policies of the French Foreign Legion in 1831-1962.
According to it, during that period, while official policy was that any foreign national can join, and due to "anonymat" even French sitizens joined quite often, but in practice recruitment, save for some rare exceptions, was restricted to European nations, and sometimes even some of those were excluded, but this were mostly due to political and ideological considerations, not racism. For example, Algerians were not accepted into Legion because for most of its history Legion was tasked with control of Algeria, and locals were thought to be unreliable when deployed against their compatriots; recruitment of Jews in 1940 was discouraged because of rising antisemitic sentiments in French North African colonies due to influx of Jewish refugees; Russian recruits were declined in the end of WW2 out of fear of Communist infiltration, and so on.
But by 1960s French colonies were largely decolonised, and recruitment policy in practice became closer to official guidelines. In 1950, by the end of French involvement in Vietnam, French Legion began recruiting Asian troops as well (although recruits from Indochina were given different headgear), and after 1962, recruitment standarts became the same as modern ones - anyone who can get to Legion recruitment offices can join. Of course, that involves getting into France first, and that itself introduces a bit of bias towards Europeans (or at least towards sitizens of Schengen states).
Of course, recruitment policy does not indicate that there were no racial tensions within the ranks - in fact, Asian recruits in 1960s being given different uniform points to some degree of segregation. Some writers (this one, for example) argue that the Legion was heavily entrenched in the ideas of white superiority (unsurprising, given that the Legion was mostly German during the inter-war period).
Thus, I would conclude that while it was theoretically possible for an non-European to enlist in 1930, it wasn't likely he would feel himself welcome there, and there was no significant percentage of non-European troops in French Foreign Legion in the first half of XX century.
