"You are young, my child."
Translation:Tu es jeune, mon enfant.
It depends. You can see older people saying "vous" to younger ones in movies, books or even in real life, from old people used to be formal with anyone they don't know for a long time.
But it's true that in common French, people usually use the "tu" when speaking to a child.
"Tu es jeune, mon enfant" and "Vous êtes jeune, mon enfant" should be both accepted.
The pronoun "vous" can be used both for the first person plural and the FORMAL second person singular (conjugation remains the same).
"mon enfant" indicates that the person is talking to only one person, therefore, it means that it's the formal "vous" used in the sentence.
This explains why we don't use plural for "jeune".
Note that the INFORMAL second person singular is "tu".
"ma enfant" for a female child is theoretically possible, since "enfant" can be either masculine or feminine.
However, "ma+enfant" shows a conflict of vowel sounds [A-EN], so "ma" is changed to "mon" to better flow in pronunciation.
So, you can say : "mon enfant chérie" to address a girl.