I'm guessing that the problem might be related to your LNBs. How many have you got? If you haven't either got two separate or a monobloc, you will only be able to receive either hotbird or astra, but not at the same time, and not without moving the dish to point to the other satellite.
What's happening at the moment I think is that you have the dish pointed at hotbird, and coincidentally some of the transponders in your astra list are also hotbird transponders, so you pick up a picture. But it won't be the right channel! To test, select a working astra channel, get the transponder information, and go to lyngsat or
www.kingofsat.net to see which channel you should have on that transponder if you are pointing at astra, and which channel for the same transponder on hotbird.
I lived in just outside Paris and had no trouble at all with an 80cm and 2d.
If I am correct, and you only want hotbird for TPS and astra for BBC/ITV, The cheapest/easiest solution is a monobloc LNB for astra/hotbird 80cm dish. Set the first LNB to hotbird, and the second will automatically point to astra. If you see this as becoming a hobby, a better solution might be a motor.