Owning a 4-3 record for the tournament, Australia's combined margin in losses totaled just nine points and they will rue the what-ifs as a couple of late missed shots proved the difference between a potential medal and sixth place.
Leading by three points at the final change against France, Australia's offence dried up as they did not hit a field goal for five minutes.
France went on a 5-1 run but when Lara McSpadden (four points, one steal) broke the drought for the Gems, they re-took the lead quickly.
The match then ebbed and flowed as it hit the last two minutes before Maeva Djaldi-Tabdi put France ahead with a nice seal on the post against Ezi Magbegor.
Magbegor had the response though, tying things up again inside the last 50 seconds with a sweet post-move of her own.
A brilliant defensive sequence then gave Australia a chance to hit the game-winner but they could not find a good look before the shot clock ran out and at the other end of the floor, Jazmin Shelley was called for an arguable foul that saw France move ahead by two from the free-throw line.
The Gems had one last chance and coach Dee Butler drew up a play for Magbegor but she was unable to hit the turnaround jumper on the siren.
From the opening tip, France were keen to get out in transition but Australia were up the task, disrupting their offence with some excellent hustle.
They looked to have scouted their opposition well and restricted them to 2-17 shooting to start while an early three-pointer from Shelley had her side up and about, leading by seven at quarter-time.
Bibby (11 points, 13 rebounds) and Anneli Maley (three points, 11 rebounds, four steals) set the tone on the boards as well although France began to match Australia's defensive intensity out of the first break.
However, Magbegor (ten points, ten boards) and Bibby took advantage of some silky passing inside to maintain a two-point edge going into half-time.
With France threatening to gain momentum on a few quick baskets, the Gems went into a full-court press out of half-time but their opposition continued to charge, tying the game halfway through the period while also forcing Magbegor to the bench with foul trouble.
McSpadden came on and played some important minutes in her place though while Bibby reached a double-double as she relentlessly attacked at the offensive end.
Shelley (seven points, five assists, two steals) then hit a huge lay-up through contact in the dying moments of the third period to push Australia's lead back out to three heading into what was a thrilling final term.
Find the box score here and watch a replay of the game vs. France below.
While the overall result is the worst for the Gems since 2005, their performances were anything but disappointing and with two games, including the Quarter-Final, decided by a missed shot on the buzzer, it will surely only fuel the fire for their next tournament in 2019.