Mother Goose was not a real person, so there cannot accurately be said to be a "real" Mother Goose; most of the stories that are attributed to Mother Goose are folktales with indeterminate specific origins. Even so, there are a few different origin stories that point to a supposed "real" Mother Goose, including one that says an eighth century French queen was the real deal, but there is no real evidence to support the idea that these stories are true. In fact, the concept of a Mother Goose figure likely didn't emerge until closer to the 17th century, and the first person to publish a volume of the folktales and fairy stories commonly attributed to Mother Goose was actually a human man, not a mother or a goose.
The French queen who is commonly thought of as the "real" mother goose was the mother of the infamous Charlemagne, and she was known as "goose-foot Bertha," which may be where the association of mother and goose comes from. Another theory holds that a late-17th-century woman named Elizabeth Goose is the "real" mother goose. This woman had a lot of children and was apparently a very good storyteller, but scholars have yet to find evidence that she actually created Mother Goose stories.