I believe Claire and Felix co-own the company with some friends.
Claire and Felix are co-founders of the brand, with another couple:
https://www.young-empire.com/about/WHO
WE ARE
Young Empire is the fruit of a long friendship; Claire, Félix, Katia and James have known each other since their school days. Félix worked in events before stepping into the world of wine and has been running their own vineyard (Chateau les Crostes) with Claire for the last 7 years. James is an architect and designer and has worked on projects in Switzerland and Europe. Katia has a backround in fashion and ran an online boutique which specialised insustainable designers.
After becoming parents to 4 children, they created Young Empire, an authentic family lifestyle brand, to bring magic and joy into the lives and routines of other families.
James designed the Storybook bed system, is the artist behind the decorative mosaics and is passionate about giving children the right tools to let their imaginations run wild through the use of good design and creativity. Felix brings to this innovative project his expertise in distribution networks, sales, marketing and finances; Katia develops the branding for Young Empire and the clothing line for adults and children. Young Empire has been a long labour of love and a real team effort to transform the teams dreams into a reality for other families. Our personal values as a friend group have become the pillar on which Young Empire stands; respect for the environment and the manufacturing personnel, quality materials (responsibly sourced timber, organic textiles), magic, authenticity and simplicity. Young Empire continues to develop their distribution network thanks to trade shows like Maison & Objet in Paris, in their online shop and through handpicked retailers around the world.
Each of the other 3 seem to "bring" something to the project. Claire brings nothing, it seems
ETA: I believe it's their company and that they don't use their titles in conjunction with company dealings. Don't quote be on that second bit as I've done very little research. I tend to agree about the kids but I'm also mixed as it's their company.
They use the titles for a little of publicity. They don't use the titles on the description but the "blog" section on their website has a couple of articles associating the brand to their royal titles.