The boy sustained redden cheeks, slight bruising on one cheek, and a mark under his right eye, Sergeant Collin said.
Defence counsel Tim Cadogan said the "light slaps" were an acceptable way of disciplining a child in New Caledonia, and were legal in New Zealand "five or six years ago".
"It's a cultural misunderstanding on his part. There wasn't harm, wasn't great harm, to the victim," Mr Cadogan said.
He said the argument began because the family were about to go skiing and the boy would not wear a coat.
Judge Callaghan said: "I'm minded not to impose a penalty more than a conviction in this case.
"It is accepted that a cultural difference is really what brings him before the court, more than anything else."
Cernobori, who is due to leave New Zealand today, was ordered to come up for sentence if called upon within three months.