The judicial process that Hugo describes in The Hunchback of Notre Dame is not really concerned with finding the truth, or meting out justice. It is more to do with creating the impression of justice, and then offering up a suitable victim for the entertainment of the mob. This is seen clearly in the case of Quasimodo's trial, for example. Since Quasimodo was deaf he could not hear the questions put to him, and since the auditor, Barbedienne was also deaf, he could not hear the replies anyway.
Esmerelda was found unconscious, next to the body of the stabbed captain and was arrested along with her pet goat on the grounds of having "murdered and stabbed, in concert with the powers of darkness, by the aid of charms and underhand practices, a captain of the king’s arches of the watch, Phœbus de Châteaupers" (from Isabel Hapgood's translation).
The use of the term "murdered" does indeed seem strange here. As the OP noted, Phœbus was not killed, and this fact was known to the court at the time:
“Oh! for mercy’s sake, tell me if he is alive!” she [Esmeralda] repeated,
clasping her beautiful emaciated hands...
“Well!” said the king’s advocate roughly, “he is dying (il se meurt). Are you
The original French makes more sense. The charge is given as "meurtri et poignardé", or "injured and stabbed". So the fault would seem to lie with the translation, in particular rendering "meutri" as "murdered". Indeed, some summaries, such as wikipedia, replace "murder" with the more sensible "attempted murder".
But in fact the actual charge does not matter all that much. Esmeralda is taken from the court and tortured, and confesses to a long litany of sins, including practising sorcery, consorting with the Devil, and finally, almost as an afterthought, "murdered and assassinated" (meurtri et assassiné) Captain Phoebus. Here again "meurtri" is rendered as "murdered" in the translation. We do now have "assassiné" in the charge, which indeed would imply that Phoebus is dead. But possibly this is just the interrogators (or possibly the author) mis-speaking, since neither before nor after this charge is Phoebus stated to be dead or assassinated.
Having been found guilty by the court, and having signed a confession, there would be no call for anyone to reverse the judgement on Esmeralda. Especially for such an unimportant figure as the young Gypsy girl.