The 27-year-old Kennedy cleared a season's best 4.90 metres, fiercely pumping her fist several times after another epic battle with Moon.
"I've been very open to the media, I wasn't going to share this year," Kennedy told reporters. "I didn't want to share it this time, I wanted to win outright and I'm happy I got the job done."
Moon, the Tokyo gold medallist and two-times world champion, cleared 4.85m to claim silver. Canada's Alysha Newman went over the same height but was awarded bronze due to more missed jumps.
Kennedy and Moon decided to share gold at last year's world championships in Budapest after they both vaulted 4.90m. Moon defended the decision after scathing criticism on social media, saying the danger of vaulting increases as fatigue sets in.
"To walk away healthy and with a gold medal while celebrating with my friend that had jumped just as well was a no-brainer," Moon said in Budapest. "Part of the reason we've reached the highest level is by listening to our bodies."
Kennedy made sure there was no sharing on Wednesday at Stade de France. She failed on only vaults - her first attempt at 4.70 - before flying over the next three heights with ease.
After Kennedy's successful attempt at 4.90, Moon's only chance to steal victory was by clearing 4.95 but she and Kennedy failed at that height.
"I had a sneaking suspicion victory was in the bag after 4.90," Kennedy said.
Her victory was some redemption for the Tokyo Olympics in which a serious quadriceps injury contributed to her elimination in the preliminary round.
