Brausse (23), who was second in Roubaix 12 months ago and third in Berlin in 2020, pipped New Zealand's Bryony Botha at the velodrome near Paris, which will be used for the 2024 Olympics.
Britain's Josie Knight claimed bronze ahead of Brausse's compatriot Mieke Kroeger.
Earlier, Belgian pair Lotte Kopecky and Shari Bossuyt edged France's Clara Copponi and Valentine Fortin by a point to clinch the women's madison.
The home favourites were initially declared champions by the unconfirmed results before third-placed Denmark were awarded points, meaning the French couple lost out on gold.
"Our coach said: 'No you're winning', but on the screen it was something different," Bossuyt said. "They then told us we won, I don't know what that feeling is."
Elsewhere, French 20-year-old Marie-Divine Kouame took women's 500m glory ahead of German Emma Hinze and Chinese rider Guo Yufang.
Later, gold in the men's omnium will be won with Britain's Ethan Hayter leading in the standings with just the points race remaining.
During Sunday's final day of action, the highlights will include the women's keirin and men's sprint.
On Friday, Italy's Filippo Ganna set a new world record on his way to a fifth world title in the men's individual pursuit.
