No one can predict what the airfares to Paris will be next summer or whether it would be cheaper to fly to London and then take the Eurostar, but normally, no, it wouldn't be, plus it would be a pain in the neck to fly to England in order to get to France, unless you planned to spend time in London first.
This idea doesn't make much sense. Even *if* it is cheaper you will lose a lot of time getting to Paris on the Eurostar. I'd much prefer a non-stop flight to Paris and would be willing to pay more if I could get one.
Generally speaking flights are cheaper to LHR than CDG from NYC airports but not cheap enough that your plan would make sense.
We have done this twice and are about to do it again in December. The flights are about $200 cheaper right now That savings will not amount to much one you factor in the cost of the train tickets. We have 3 extra days this trip and would like to spend a little time in London. So for us it works out ok. I looked at taking a flight from London to Paris. I think the hassle of the airport and then traveling from CDG to Paris is not worth it. I like taking Eurostar and arriving in the center of Paris. If you have only a week or less then I recommend going directly to Paris.
We've done this several times. However, they were all combinations trips with London being a 4-5 day stop. If you are planning on visiting London as ell as Paris, do as previously suggested and make it a multi-city trip catching the Eurostar to Paris. If however Paris is your only destination, fly in/out of CDG.
I've looked at it several different ways over the years from Washington DC for cost-effective business trips and I always end up with the round-trip to Paris being my best bet. I still always look though (for business - I'll pay up for less hassle for personal trips) in case one of the carriers has some fantastic airfare special.
I don't think the hassle to do this if you are not interested in seeing London is worth the possible (probably slight) cost savings.
I'd love to have the option for a non-stop flight to Paris but unfortunately there are none from Phoenix so maybe my opinion is skewed from being envious that you even have that!!!
The only way to know that is to prudently shop fares for both flights and Eurostar for Your Dates.
If you are convenient to JFK, have a look at Aer Lingus. Though there are non-stop flights with AA or Air France from Boston, Aer Lingus is my new favorite airline, even though there's (a totally convenient) connection in Dublin both ways. Ordinarily, I would prefer non-stop. But, I've been saving 2-400 per ticket with Aer Lingus and actually enjoy the "break" in Dublin, along with Terminal 1 at CDG (a dream compared to the others).
When you add up the air fare, airport transfers from Heathrow (which are costlier than Paris), Eurostar fare, you'll not save very much, and keep in mind that you'll have to drag yourselves from Heathrow to the train station.
I would choose CDG over Heathrow anytime, even if it does sound fun to take the Eurostar. I wouldn't voluntarily fly into Heathrow unless I had no other options.