I travelled recently to India via London and went thru the same situation.
I called Air India to find out if air transit visa is required and gor mixed answer. Some people said not required some said required. One person explained that since you don't have to come out of plane in Paris , you don't need. But if some situation arises where they ask you to come out of plane in Paris , there could be a problem.
I had Canadian PR. I called French embassy and told them about my Canadian PR and Advance Parole document. I was told that I don't need transit visa. In fact lady confirmed with somebody and called me back in the evening just to tell me this. I am not sure whether I was exempted because of Canadian PR card or advance parole.
I called British Embassy and told them about my Canadian PR card and I was told that transit visa is not required in that case. So finally I travelled by British Airways and returned back without problems. I had to show my Canadian PR card at check-in.
Guys, I am not sure if I made any sense or am of any help but did go thru the pain / confusion you guys are going.
My suggestion, call the embassy and ask as its them who make rules.
Don't worry about 3 copies, carry all of them. I was coming from canada on AP and immigration officer kept 2 and returned me 3rd. I used 3rd to travel to India recently.