The French word "bêtise" means something like a small act of naughtiness (frequently used for small misdemeanours of children). I'm struggling to think of an equivalent word that could be used with an anglophone child.
Folly and follies.
Bêtise derives its meaning from the word bête, literally beast – and in fact the words are related.
A literal translation, then, would be beastliness. In some situations that word might be the right choice. But when you want a translation that connotes harmless misdemeanors, it is not adequate for two reasons: (i) it does not so much connote harmlessness, and (ii) it is not countable.
But you can use the same conceptual metaphor: describing a person or his behavior by equating it to the behavior of something base, be it a class of persons, animals, plants, or whatever. English has many words that employ this metaphor: follies, foolishness, idiocy, imbecility, stupidity, tomfoolery (like a mentally deficient person), brutishness, bestiality (like an animal), and so on.
The advantages of folly are that it is countable (can be used in the plural, in a sentence such as: “Enough of your follies; go to your room”) and uses the same conceptual metaphor (equating the person's behavior to that of a fool), while at the same time it connotes relatively harmless foolishness rather than dangerous behavior.
Translation of words is often difficult because sometimes They Just Don't Say Things That Way.
If in French you often refer to acts of naughtiness, in English correspondingly you talk about -being- naughty.
In French you probably say somewhat translated "stop with all your bêtises", but in English you'd say "stop being naughty" or "stop your foolishness". 'Naughty' is more about breaking rules or breaking things, and foolishness is just about being impertinent or not serious.
But those two phrases are somewhat out of date. The preferred locution (at least in GenAmE) nowdays would be
(the latter is of course more about breaking rules, and is advice, rather than after the fact).
As an aside, there is a literal translation, 'stupidities', but that is not really a recognized word in English. There is also the literal translation of 'small act of naughtiness' which is 'peccadillo' which is not really used for childish acts.
The usual word for disobedient but generally harmless behavior is mischief. Note that this is a collective noun: Tom Sawyer commits mischief, commits five mischievous acts, or is known for his mischievousness, but he does not commit five mischiefs.
Children known for their mischief may alternatively be known for their high jinks, monkeyshines, or naughtiness, or they may be guilty of shenanigans or tomfoolery.