As you are in transit from a non-schengen country to another non-schengen country their is no need to clear customs and immigration in Paris. Your checked baggage will almost certainly be checked through as you appear to be on a single ticket. When you check in in SCL ask them, and then check the luggage tag. If it shows CDG and LHR, no worries. If it shows only CDG you will have to claim it in Paris, and 1h40 will not be enough.
You will have to clear security with your carry-on. This has been reported to be difficult but you should be OK.