The interview process is fairly simple: phone screen with HR to discuss interests and outline the role, followed by in person interview at their NYC HQ.
During the in-person meeting, you'll meet with HR and if that goes well, the hiring manager you'd report to. HR is mostly concerned with ensuring the right fit for their specific company culture. E.g. why you want to work at a European, privately held company, understanding you're aware of the relationship between the Paris office and the NY location, what your personal work ethic and values are.
One thing that was frustrating is that Chanel is very opaque about corporate roles and structure, meaning the job posting had vague qualifications and the phone screen wasn't elaborate either. Only until I got to the meeting with HR, and then moved on to the hiring manager I'd report to, did I realize I was interviewing for a position that was very junior in the context of my graduate degree and compensation needs.
Also, the conversation with that hiring manager was...interesting. Coming from a fashion background that was "extremely impressive" (their words), I was still asked "what do you think of the house of Chanel?" and "What do you think of Gabrielle Chanel?" I get that they might be screening out candidates who just want to work at Chanel and aren't familiar with the brand, but it didn't make me feel warm and fuzzy to feel I was already being spoken a bit down to before even starting a role.
Ultimately I declined moving forward with the position, and HR was supportive. I guess my one piece of feedback would be to employ better screening practices in explaining the organization, role, and salary structure over the phone to avoid wasted in person time.