The 25-year-old posted 7.10 metres to take the title from Tokyo Olympic gold medallist and three-times world champion Malaika Mihambo of Germany who claimed silver with 6.98m.
American Jasmine Moore jumped 6.96m to secure bronze.
Davis-Woodhall had victory locked up before her final jump, choking back tears before her final sprint down the runway. She stood up briefly after landing, then fell back into the sand with a wide smile to the delight of the Stade de France crowd.