Hi!
It's been quite along time since I saw a doctor in France, and I never went to see a gynecologist in France (I wa too young). But almost all the doctors I had in France were very friendly and caring, so I'm sure you'll be fine. As to the medical system there, I also think you'll have no big surprise if you live in Hong Kong because I think Hong Kong's medical system is much westernized (considering that many things are very different in Korea compared to both France and Hong Kong).
Also, in my opinion, you won't have any problem about getting a letter either, especially when you tell them you have to return home.
Finally, I used to be perfectly bilingual, but I haven't spoken French in years!