Sometimes you can get virgin for around 3000 or so and sometimes even less if you buy a virgin ticket on QF
But to be honest, i really wouldn't could on it especially in the summer.
Now you could fly Air France for 2500 to paris in their business class but I think you'd have to get on the 744 for the lie flat seat and at that, not all the 744s have been retrofitted. You'll need 50 day in advance booking on AF
but then you'll also have to figure out how to get to London from Paris.
Lufthansa is another option, around the same price if you book way in advance on them, but again, not all the 744s have been retrofitted with the new C class and I don't know about the 343s. Still though, you'd have to find some way to get to London from Frankfurt or Munich.
PARIS, FRANCE...THE BEIRUT OF EUROPE.