OK, Delta doesn't fly into Heathrow or go between LHR and CDG?

So I could redeem miles with the Sky Team partner airlines as I understand it.

I was thinking of flying into LHR (from SFO or SJC), stay a few days and then go to CDG and then return to SFO or SJC from Paris (which BTW still seems much cheaper than New York despite the Euro-Dollar exchange rate these days).

I briefly looked on the Skyteam.com site, and it appears Continental goes directly to LHR but Air France seems to want to make you go to Paris and connect to LHR.

Now I could always go to Paris first and then London but I'm guessing on AF, they would have me fly back to Paris before making the hop across the Atlantic.

Anyone try a similar itinerary with the Sky Team airlines? I would imagine it's not that unusual so you'd think it would be more easier to set up than it looks like.