I do want to sympathise with you, but this has nothing to do with BA and I don't see why they should compensate you.
- It's no different if you, for example, drop your printed boarding pass in a puddle as you exit the taxi and a dog pees on it
- As others have pointed out, you need to add the BP to your passbook
- BA will have wording that absolves them from website/app tech issues relating to you checking in, and
- Why couldn't you use those third-party electronic kiosks they have at Orly after the lounge but before security?