Historically Vietnam had conquered parts of China. However, I think a Partition couldn't work in the same way as say the Partition of Poland.
I think it'd have to include a number of Asian groups to succeed - which isn't impossible, but difficult considering the initial arrangement.
But say you have France via Vietnam, Britain via an attempt at Tibetan Protectorate status (i.e. use them as a proxy), Japan, Spain, Netherlands, even Russia.
You've got a lot of people there with competing interests.
As a stab, some 'transfers'
Tibet - Total control over the Plateau. They'd probably be interested in the Taklamakan Desert and Kashgar.
Russia - They'd probably want the Takklamakan Desert and Kashgar too. So yay...
Japan - Korea, and probably the territories around the Yellow Sea.
Spain - Taiwan is negligible, but interesting. Parts of the coastline perhaps. They seem like they could be sidelined however.
Netherlands - Coastal cities are their best friend.
Vietnam (France) - The Pearl River Delta, Valley, and surrounding territories.
In this the three largest land transfers beneficiaries are Vietnam, Japan and Tibet. I can't see anyone too eager to control the deeper inland territories in China besides maybe Japan and Russia (but those two would be direct conflict for them). As a result, I think you'd find a China that is a shadow of its former self left as a rump as the most likely end goal for all parties. A rump state that most trades via Japaneses, or French ports. (Maybe the Dutch, just so they can be difficult).
I honestly expect this isn't possible, but a Netherlands with intermediate coastal territory between the Vietnamese territory and Japanese Territory, and a larger Tibet seems the likeliest way to partition it. In which case, the history of a China that has rail lines between itself and the Dutch cities could be interesting. Dutch as a second Chinese language?