Ah, so are you indicating that we will be in a transit area when we get off the plane from Chile and before we get onto our final flight to London and hence immigration will be in London and not Paris?
The final point you make is the nub of the 'argument' if you like, if we don't know whether our luggage is going to be checked all the way through to London when we depart Chile when we are standing in the check-in queue, it will too late to make alternative arrangements in Paris if that is where it is offloaded for us to pick it up.
If our luggage is off loaded at Paris and we have to pick it up and re-check it back in for our final leg back to London, who's responsibility is it to ensure we get on the scheduled London flight, and if not, who is going to make the alternative arrangements to get us back to London? I hope my post is clear to the team.