Michaela Blyde, Gayle Broughton and Stacey Fluhler all crossed for first-half scores for the Baby Ferns, Caroline Drouin pulling one back for France to leave it 19-5 at half-time.
Anne-Cecile Ciofani notched up France's second shortly into the second-half, but New Zealand's grip on the game never faltered as Nathan-Wong converted her own try to seal gold, one better than the silver they won in Rio in 2016.
"I have looked at my silver medal (from Rio) every day since I have been here," said Kiwi Ruby Tui.
"I will never forget the person I was when we won silver because I have had a complete change in the person I was then in order to win this gold.
"The gold is a metaphor for a dream about positive thinking. It is not just the gold medal but how we have grown since. You just have to believe."
Fiji, whose male compatriots won the men's gold, beat Britain 21-12 for bronze.