So the whole thing is not very clear and be aware that it will take a major while (half a year is not a bad estimate, some travels to HK possibly as well) to get your "Home Return Permit" (HRP). Also it does not help that rules changed some years ago.
Most of what I am writing is based on forum entries here and here, so no official info and not from my personal experience.
Your eligibility to receive a HRP is as follows:
- You should be born in HK.
- You should possess an HK birth certificate
- You should have any certificates showing that you are a NATURALIZED HK CHINESE CITIZEN.
- You should have an HK PERMANENT IDENTITY CARD
- You should have an HK PASSPORT
if you have dual citizenship with any other country, for example hk passport with a US passport, that is fine, as long as you can still meet the requirements stated above.
I've seen somewhere (was it wiki that you quote) that you can apply at any Chinese embassy but the forum entries make it more likely you would need to go to HK, and likely more than once. It's long stories and read them yourself, and contact your local Chinese embassy whether you can apply with them.
The crucial point apparently is the other way round: once you had a HRP, you are no longer eligible for Chinese visa. And one more point that could be crucial for you or not a big deal: if you decide to get the HRP you are no longer under the consular protection of France in your case while in China.
In your case I would well consider whether the trouble of getting the HRP compared to regular visa on your French passport is worth it. If you do decide to get the HRP, knowledge of Chinese will surely help.