"J'aide mon enfant."
Translation:I am helping my child.
They are as informal as one another.
Words rarely have perfect one-to-one correspondence across languages, and the fact that the relative frequencies of the pairs of words in writing are very different point to that being no different here.
"child" is 13 times more common than "kid" in published books; meanwhile "enfant" is 69 times more common than "gamin" in published books. That means that for every use of "gamin" one would expect English-language authors to have used "kid" 5.3 times. In short, to keep the word usage frequencies the same between languages, the most common translation of "kid" by far would be "enfant," which would be used in over 4 out of 5 instances.