Final and last are usually interchangeable, but final is the stronger (and somewhat more formal) word. Last is more common, but there are circumstances when one would prefer final - usually to express the absolute end, when there is no doubt that this will be the end of whatever is under discussion. "That is the last cake" does not mean that we will never again see a cake; "that is the final cake" could mean there will never be any more cake in the future (or it could be a parent telling a child in mock-seriousness "That's your lot!"); but, either way, it is the stronger expression.
Last and finalcan also refer to something that happened in the past. "During the last war, food was rationed in Britain" (past)
"At the end of the the last war we will negotiate an abiding peace" (future)
"In the final conflict, nuclear weapons destroyed (or will destroy) mankind" (past or future, but in either case, definite and without doubt).
Since "gamins" has been added to the course, there's been an effort to teach that kids/gamins is more casual, and children/enfants is a higher register of speech. Indeed those are the best translations. If kids/children are both accepted for enfants, that distinction is lost.