Playing against compatriot Laura Hodges, O'Hea and her side bounced back from a Game 1 loss to take the following two contests and clinch the title.
O'Hea can add the Championship win to two WNBA titles as well as a bronze medal from the 2012 Olympics.
In Game 1, Bourges jumped out of the blocks to take control within the opening minutes of the game and then held their opposition to just six points in the final period in a strong defensive effort to win 54-49.
O'Hea collected two points, four rebounds and an assist but struggled from distance, missing all four attempts from the three-point line.
The small forward was instrumental in the Game 2 victory though, recording nine points on 4-6 shooting in 24 minutes. She added six boards, an assist and a steal to that tally as Lattes Montpellier used a dominant first half to run out 61-51 winners.
In the decisive Game 3 this morning, O'Hea and her club had one hand on the trophy at half-time, leading by seven points.
A stirring fight back from Bourges tied the match up though at the final break before the lead changed hands several times down the stretch. Anael Lardy was the hero for Lattes Montpellier, hitting two late free throws to snatch the 63-61 victory as O'Hea was crowned a French champion.
The Aussie had another nine points in Game 3, again proving her worth at both ends of the floor with a three-pointer and two steals. Hodges also had her most influential game of the series off the bench, adding four points and two rebounds as her team fell just short.
O'Hea has had little time to celebrate her success, heading out on a plane to join the Seattle Storm for the 2016 WNBA season while Hodges will now focus her efforts on the Australian Opals as they continue their road to Rio.