When talking about the simple fact of children crying, that is screaming, as in the sentence "Elle entend … des enfants.", you say usually "les cris des enfants", "les cris de l'enfant" (if there is just one child) (ngram). Nevertheless, in this sentence "cri" can also have other meanings, depending on the context.
Both can work depending on the context, take an English analogy like "I see the agony of these people", surely there is more than one in that situation.
In this, it depends on the context too, if she is in a place and hears kids screaming nearby, so she is hearing a scream aka le cri, but if these kids are being mistreated so she is hearing their ...
Beware that crier is a partial false friend and only means "to shout/to scream", not "to weep".
Singular is possible here and means either a synchronized scream or a generic scream, the idea being no individual screams are referred to.
She hears the children's scream/shout.
Luke also rightly says if each child only shout once, the ...
Generally, if each person has only one, French uses the singular.
The language is happy to distribute the noun to all the people in question, like the multiplication of the loaves loaf.
Case in point: There's a line in La peste where he's talking about a crowd and says something like:
La crainte se fit voir sur leur front.
"What?" you say. "...
"Voici un grand chat sur la table." — Here is a big cat on the table.
It is a cat, and it happens to be big.
"Voici le grand chat dont je vous ai parlé." — Here is the big cat I told you about.
Of all cats, it is specifically the one that is big.
You have to understand a basic principle before going too far in the study of a language. Just as in your mother tongue the forms used have been handed down to the users of the language from a long tradition, although as time went by some changes were made. The forms we use today correspond to fixed meanings and that is all there is to it : you are dealing ...