No, Esmeralda is not Quasimodo’s mother. Pending on what version is question Esmeralda is four years younger than Quasimodo in the book. In the Disney version while she may be maternal towards Quasimodo we know she is not because we see Quasimodo’s mother die.
But who is Quasimodo’s mother? In the Disney we see a young women who just wanted to get her child in Paris for a perhaps a better life. But what were her hopes, fears, ambitions, desires? What was her favorite color, foods, pastimes? The real tragedy is we never got to know her as a character.
In book we only know that Quasimodo’s mother was an unfeeling vile women who abandoned him as baby. But Maybe she died in childbirth and some other relative abandoned him. Maybe she was lied to and she was told her baby died at birth and then he was abandoned.
We’ll never know the truth regarding Quasimodo’s mother but one thing we do know is that she was not Esmeralda. Unless that was her actual given name and then I guess the answer is yes but what are the odds of that?