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. "How can the whole crowd have one forehead?" So you take the liberty of rewriting it:

La crainte se fit voir sur leurs fronts.

"What?" says a Francophone. "How can people have multiple foreheads?"

So you leave it as it is and forge on a little bit wiser…

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 singular is common.

Without context, it is hard to tell what happened, but say if all kids are watching a show/movie and a monster suddenly appears, they will all emit a loud cry at the same time. That would be a case where the singular is better.

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 screams translated to les cri. Usually les cris is used when someone is distressed and shooting for help.

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.

The word "cri" has two meanings that are very close to one another and if the writer, not conscious of that or careless, does not take care of ensuring the existence of a proper context there can be ambiguity in his/her text.

The meanings can be extracted from the TLFi.

A.− Son(s) généralement bref(s) et aigu(s), émis instinctivement par les cordes vocales sous l’effet de certaines émotions.

1. Expression phonique d’une sensation, d’un état physique ou moral, ressenti en profondeur très intensément.
2. Son de voix caractérisant un animé et, p. ext., une situation, un événement.

In "1." the word is taken as meaning an occurrence (expression phonique) of the particular sound called "cri"; in "2." the word is taken as the sound, not in individual instances of hearing it, but as a sort of sound particular to a creature (caractérisant un animé).

In the sentence "Elle entend … enfants.", since "enfants" is in the plural the meaning of "cri", out of the two, must be that in "2.", that is "type of sound" (here produced by children).

Here are examples for the case "sound".

(ref., 1910) Au point de vue du diagnostic et de la symptomatologie, M. Sisto insiste sur un signe nouveau qu’il a le premier signalé à Buenos Aires avec le Dr Gaing, à savoir le cri des enfants hérédo-syphilitiques. Ce cri, incessant, de jour et de nuit, …

(ref., 2013) Des milliers de tentes, maintenant, se tenaient serrées le long des remparts, dessinant d’immenses faubourgs de tissu multicolores où se mêlaient le cri des enfants qui jouaient dans le sable et les braiements du bétail.

(ref., 1997) Qui n’a jamais regretté, en se promenant dans un centre-ville restauré, de ne plus y entendre le cri des enfants qui jouent, chassés avec leurs parents par des loyers prohibitifs ? Les modes de vie à venir inciteront à relancer la construction …

Examples for the case "occurrence"

• Le cri d’un enfant la réveilla mais ne fut pas répété et elle se rendormit aussitôt.

• Les cris de ses enfants l’irritaient maintenant et elle ferma la fenêtre.

Another possible explanation is given by the figurative meaning of the word "cri", that is when "cri" means something as in "cri du cœur" (cry of the heart); there is hardly any context possible for a plural if that is the meaning to be given to "cri" in "Elle entend…"; the almost unique context is that of children (rather mature children) who are having a collective concern or problem.

Example

(ref.) Et Dieu aujourd’hui, c’est le cri des enfants irakiens.