Upvote:6
It's perfectly safe. Qatar Airways flights from Manchester to Doha actually do not pass over Libya or Egypt, but skirt east of Syria and Iraq by flying over Iran: https://flightaware.com/live/flight/QTR22/history/20160801/0800Z/EGCC/OTHH
This is precisely the same route as that flown by Etihad's Manchester flights: https://flightaware.com/live/flight/ETD16/history/20160801/0810Z/EGCC/OMAA
I'm also not sure why you're worried about Paris, it requires very heavy weaponry to hit an airliner flying 10 km overhead.