What is the ruling on a man working as a partner in a women's hair and beauty salon (coiffeur) to manage it and sell beauty products therein, knowing that he has no experience in this field?

It is not permissible to sit in a place where women mingle or where one might gaze upon what is unlawful to gaze upon of them. However, if the establishment and the sale of cosmetics are regulated by Sharia-compliant controls and free from prohibitions, then there is no harm in establishing and managing it.