I believe that the US/LHR boarding pass will still let you buy it at duty free prices at LHR since you just got off an INTL flight, and they will allow you to take it on the plane as carryon as long as you buy it inside your departure terminal. I don't think the US/LHR BP will still work at CDG, however, since you're arriving there on a flight from the UK. Buying it on the US/LHR flight won't work since you can't take it through security when you change flights, and your bags will most likely be checked through eliminating the chance to put it in your checked bags. Other than taking it with you from the states in checked baggage, LHR seems your only option other than in Paris at street prices.

But, why waste duty free on Vodka? There's a wonderful Whisky shop at LHR that sells otherwise hard to obtain brands. You can buy some potatoes when you arrive in Paris and make your OWN vodka!