- Khadija Shaw (90'+2')
The fifth-ranked French, semifinalists at last year's European Championship, were unable to get their game going as the Jamaicans hassled and harried them throughout the 90 minutes to earn their first World Cup point after three losses on their 2019 debut.
Forward Kadidiatou Diani almost clinched the winner for France in the 90th minute but her powerful header hit the bar then the post to the delight of the crowd of nearly 40,000, who had embraced the 43rd-ranked underdogs.
"It was a difficult first half, we came up against a group of really athletic women," France coach Herve Renard told reporters.
"The second half was better, we created chances but unfortunately we were unable to find the back of the net."
The Jamaicans celebrated at the final whistle as if they won the tournament, even though they lost their best player Khadija Shaw to a red card in stoppage time.
Coach Lorne Donaldson thought the draw would rank as Jamaica's finest football moment.
"I would say it is the number one result we have had so far. I think it's the number one I have seen, men or women. I would put it there," he said.
"Just looking at the rankings, that result on this stage has to be number one."
It looked like the game might be robbed of its two biggest names when France skipper Wendie Renard and striker Shaw clashed heads in the opening few minutes.
Both returned to the pitch after brief medical attention, however, and Shaw was soon causing France plenty of problems with her direct running and physicality.
France put together the first move of any quality in the 36th minute with forward Diani set free to draw a save out of Jamaica goalkeeper Rebecca Spencer, who was again at full stretch to deny Renard at the ensuing corner.
France gradually imposed themselves on the game in the second half and Diani and midfielder Sandie Toletti both had chances before the hour mark but neither bothered Spencer.
Diani steered another header wide in the 66th minute and Eugenie Le Sommer drew another save out of Spencer 10 minutes later as the rain cascaded down on the pitch.
Outstanding left back Deneisha Blackwood led the way as Jamaica kept to their task, however, and they held on as France lofted cross after cross into their box in a frenetic finish.
Shaw, who had been a constant thorn in France's side, was sent off when she received a second caution for a tackle on Renard deep in the France half.
"I am satisfied with the attitude of my players, they showed fight and that will be important for the challenges that come ahead," added coach Renard, who masterminded Saudi Arabia's upset of Argentina at the men's World Cup last year.
"We deserved to win, they didn't get any chances. I hope (Jamaica) fight as hard against Brazil and Panama."
- María Carvajal