Can you travel from A(Europe) to B(China) to C(Japan) back to B(China) and back to A(Europe)

Of course you can. You should just have in mind that when using 144 hour visa free transit you are allowed to stay just within one mainland China transit area. In other words, your itinerary from Europe to Japan is allowed to have just one city area and also for your itinerary from Japan to Europe. In other words, you can visit first Beijing when traveling to Japan and on your way back, you can visit, for example, Shanghai, however, you cannot visit both during one sojourn in mainland China.

Also, I encourage you to use correct terminology because it is 144 hour visa free transit and not 144 hour visa or better to say, there is no any kind of visa at all.

By the way, if you are a French citizen, then you do not have to bother with these details because French citizens can travel to China visa free for stays of up to 15 days.