Coming of Age means?
Tricky, there is no exact translation in French for this
expression, but it is "roman d'apprentissage" (or sometimes "roman
initiatique" or "roman d'initiation") for books. A typical French
classical novel ("roman") in this category is Flaubert's
L'éducation sentimentale.
Applied to movies, "films d'apprentissage" is not right, "film
initiatique" would fit better. But again, it's not just "coming of
age" on its own. "Apprentissage" (apprenticeship) or "initiation"
(without "roman" or "film") would not be correct either. Maybe
"Histoire (story) initiatique" could apply to either books or
movies.
But the connotation is not the same as English. "Apprentissage"
or "initiation" both refer to some kind of usually soft and smooth
education process, under an adult's guidance, not a traumatic
family or sexual event as is sometimes the case in such English
stories.
Sometimes "passage à l'âge adulte" is used, but it is very
cumbersome, formal, and limited to teenagers becoming young adults.
It does not include children who grow out of childhood and suddenly
become more mature, but do not become adults, as is sometimes the
case in coming of age stories.
I think French should use "rite de passage" (rite of passage),
which has been used to describe the formal coming of age ceremonies
of the early tribes. And it somehow manages to have the word "age"
in it... ^-^