France needed overtime but finally saw off the challenge of Hungary to win qualifying Group C and clinch a place in next year's EuroBasket Women in Riga, Latvia.
Celine Dumerc had 12 points and 10 rebounds and also came up with three steals as the French prevailed 68-64.
Playing in Bourges, where Dumerc and some other national team stars also compete professionally under the same coach, Pierre Vincent, the French had a nervous finish.
Endene Miyem, one of the Bourges players, drew a foul with six seconds remaining and went to the line with France trailing 58-57.
Miyem missed the first but made the second, and Vincent called timeout.
When play resume, Hungary's Zsófia Fegyverneky turned the ball over and the final buzzer sounded to signal overtime.
The lead went back and forth until another Bourges player, Emmeline Ndongue, made two free throws for a 66-64 lead with 10 seconds left.
Vincent called timeout again to discuss the end-of-game strategy, and when play resumed, Orsolya Englert turned the ball over for Hungary.
Florence Lepron, a former Bourges player, added two free throws with seven seconds left to finish the scoring and leave France with a 6-1 record.
Hungary slumped to 3-3. They finish with games against Romania and Croatia, while Slovakia (4-3), have one game left against Croatia.
If Hungary and Slovakia finish with identical records, the latter will win the head-to-head tie-breaker to come in second.