Round trip to Taiwan with return visa China for 6 days/144 hours??

Hi,
I'm planning the following itinerary for April-May:
Paris - Taipei
Taipei - Shanghai
(Shanghai to Beijing by train)
Beijing - Paris
Can I benefit from the 144 hours free transit while in China?
Can I travel within China i.e. from Shanghai to Beijing and leave from Beijing back to Paris? Or do I have to fly out from the same city (Shanghai) in which I entered China?
Thank you very much,
Clémence