I'm thinking about getting a round trip flight as follows:
JFK to LHR
LHR to CDG

CDG to LHR
LHR to JFK

I'm going to start my holiday in Paris, but I'll be ending up in London. Am I allowed to start my return flight with the LHR leg so I don't have to return to Paris just for the flight? I'd appreciate some advice on this. Thanks.

No, you can't.

These days, open-jaw tickets usually don't cost more than standard roundtrips. Just do a search for a multiple-destination trip for JFK-CDG and LHR-JFK, and get the tickets issued that way.

Above is correct - if you do not show up for first leg your second leg will be cancelled and you will be swimming home.

However, many airlines would consider an itinerary in which you fly INTO Paris but BACK from London as a legit round-trip, i.e., charge you the same as they would coming back from London.

Plug in JFK/LHR/CDG paired with CDG/JFK for your round-trip itinerary and see if it doesn't cost essentially the same as your original itinerary.

In other words, what rkkwan said.

What others have said is correct.

But some airlines do allow stopovers, where you can spend some time in a place your flight passes through, so you could also look for a return leg CDG to LHR, LHR to JFK, with a stopover in London.