Upvote:0
Beijing and Manchester are both international destinations (i.e. outside the Schengen area). CDG has international airside transfers between all terminals. If you have no carry-on, then from terminal 2E, walk or take a shuttle to terminal 2C, then take a shuttle to terminal 1. You won't need to clear immigration in Paris.
If you have luggage that isn't checked through, then as far as I know you'll need to pick it up at the same place as everyone else, and that's after immigration. So in that case you will need to spend more time in a queue, and you will need a transit visa if your citizenship and visa status requires it.
If everything goes well, 3:40 hours is enough. Say 1 hour to clear immigration, Β½ hour to reach the other terminal, you have 2 hours to check in for the next flight. With a small child, it may be a bit tight as it doesn't allow much slack for accidents or for resting. The problem is if your incoming flight is late. I strongly recommend to either get the ParisβManchester flight on the same ticket or to allow a lot more time in Paris.
Upvote:1
To pick up luggage, you always have to clear immigration, so you will need a visa.
Even if you only have hand luggage, with separate tickets check-in staff will usually treat Paris as the final destination and deny you boarding without a visa.
So what you need is a short-stay (type C) Schengen visa from the French embassy. If the application form asks for the purpose of the trip, select "transit"