There is no duty-free for flights within the EU -- it is one economic area. So duty free only applies to flights outside the EU. The "duty free" shops will sell you goods, but at a higher EU price, which is generally higher than the street price (hence the advice to buy it in Paris). There is no duty free shopping upon arrival in CDG (at least hasn't been for the terminals that I have used), but you would have to fly DL non-stop to CDG to be eligible to use it, in your example, even if there were.

You can buy duty free in US or on the flight to LHR as long as you check it for the LHR-CDG flight....otherwise LHR security will confiscate it. For vodka it really isn't cost-effective (most US duty free prices are high for vodka).