Quick history of Chanel and Bourjois.
When Coco Chanel had her No5 perfume created, she went into a dodgy partnership with the Wertheimer Brothers who own Bourjois. They financed everything from production to department store stands. In return, Coco Chanel would receive 10% of all profit and no control.
During WW2, the Nazis took control of all Jewish businesses in France and Chanel used this to try to get back Parfum Chanel arguing that it was hers by name and by birthright (being Aryan and Christian). (She even became the mistress of a senior Nazi officer to help get it back). Countering the Nazi Jewish Mandate, the Wertheimers gave full control of Bourjois to a Christian French businessman so the Nazis could not do a thing about it. After the war, he gave back control.
After the war, Coco went into hiding in Switzerland as she had been marked as a collaborator and from there, she went through the courts to get Chanel Back. Eventually, she and the Wertheimers came to an agreement where they would pay all her expenses for life, all profit from wartime, 2% of all worldwide profit from Parfums Chanel and the freedom to create her own inhouse perfumes. The Wertheimers got to keep No5 and create their own Chanel branded perfumes and cosmetics to go alongside Coco's perfumes.
So, Chanel doesn't own Bourjois, Bourjois own Chanel.
However, the Bourjois name is being sold to Coty who will continue production of Bourjois cosmetics and Bourjois will continue to produce Chanel perfume, cosmetics and skincare.
The cosmetic industry is complicated. Brands names switch companies all the time.
All from Chanel: An Intimate Life by Lisa Chaney.