The Kiwi pairing lived up to expectations in the A final taking the lead in the third quarter of the race before storming home to take the win in a time of 6:53.01 minutes.
Great Britain were about one second back in second place and South Africa finished third.
Julia said it was a great feeling winning back-to-back world titles.
"We're so stoked. We're double world champions now. We're very, very excited - our smiles say it all," she said.
"I had full confidence in Sophie.
"Going through halfway we were all pretty level but I was very confident in our last 500 metres. We talked about it before the race and Sophie really ramped us up and she got us going. I think it showed in the race. We took length after length so we're really rapt."
Julia's dad, Harry, watched the race at their family home in Rotorua, with his son and brother, and was over the moon with the result.
"We are really thrilled for Julia," he said. "[Her brother] Chris was talking to Julia this morning and she said at 800m they hit their straps and everything went to plan."
He said there were "no words to describe" what it was like watching your daughter claim a gold medal at the world champs.
"I said to the staff at work on Friday night all I want for Father's Day is gold," he said. "It was unbelievable. It is just unbelievable. It had been such a competitive regatta."
He said his wife, Sue, had travelled to France for the world champs to support their daughter. While it is still a year away, Edward and MacKenzie are now clear favourites to win gold at the 2016 Rio Olympics in the women's lightweight double.
The two have also been invited by Rowing New Zealand to visit the rowing venue in Rio this week, after qualifying for the Olympics following their performance at the world champs.
The formidable pairing of Hamish Bond and Eric Murray also won a gold medal for New Zealand on Saturday night in France. During the final day of racing, starting late last night (NZT), another six Kiwi crews were competing for medals.
