Need visa to go to China transition from Taiwan to HK ?

Hello,

I have a French passport and want to go and visit my parents in Shanghai from Taiwan.

Do I need an entry permit, even if I just visit for 3 days ?
I heard I can only get visa exempted if I transit in Shanghai. Would it work if my flight back to Taiwan transit in HK for example ?

Also, where can I get an entry permit to China from Taipei, and how long does it take ?

Thanks !