@bpred said:

What language was the Beggar Woman speaking? Was it actually Lao? And what was she saying? I am curious to know more about the only non white character in the movie.

This article says that she is Laotian, so it stands to reason that she is speaking/singing Lao. Here is a part of the article:

"These cramped, rotten quarters make manifest mentions of a nearby leper colony, while sensory descriptions of the howling beggar woman and the lepers summon Anne-Marie’s inner turmoil and vacancy: “Lepers burst like sacks of dust, you know / Don’t suffer? / No, feel nothing.”"

https://mubi.com/en/notebook/posts/close-up-on-marguerite-duras-s-india-song