Airfare

Easy peasy. London to Paris by train is 2h 15 minutes. Slightly longer from Amsterdam. In both cases about 1 train per hour, you have plenty of choice.
I recommend if you do this you stay one night in London or Amsterdam, that way you avoid problems of trying to connect with a train when you cannot predict when you will arrive in the city centre.

Trains from London to Paris are operated by "Eurostar", website here: https://www.eurostar.com/
Trains from Amsterdam to Paris are operated by "Thalys", website here: https://www.thalys.com/

I do this a lot, Rule one is you have to accept the risk. My risk is if the flight from Atlanta to LHR is dramatically delayed I may be paying for a full fare rail ticket on the Eurostar to London. I am willing to risk it. SO if you can accept the risk here are my personal guidelines.

1. Allow LOTS of time. My rule of thumb for a connection like this is 4-5 hours.
2. Look into flying from LHR to Paris. My flight in October was $49. (It was so cheap I bought two, the "risky' one 2 hours after landing and the "safe" 5 hours after landing :) ) It's easier than getting to St. Pancreas IMHO.
3. carryon. Seriously it saves a TON of time at LHR if you are not waiting an hour (no I didn't make that up, I have done it!) for your luggage, plus if you are checked in to your LHR -CDG flight you can just wheel your bag following the connecting passengers sign (I either check in before I board in ATL or after I land in LHR on my phone)

On the return you must come to London at least the night before departure. The "risk" if you decide to fly in the morning of your flight from London to Houston is that when the Paris to London flight/train is delayed you get to buy a full fare one way ticket home. $$$$$$ I take the train and spend a night or two in London before I fly home.

I've done this too. I prefer to do a mini vacation in London spending a day or two.

If you decide to continue on the same day then please do allow a good time buffer for delays.

As for LHR the passport control wait can be long. The last time it took about 45 minutes to an hour but it's usually about 20 to 30. I find that due to the wait for passport control the wait for checked bags is short. Often bags are already there waiting for me.

There is no reason for airfares to be that different. Something else has to be going on. Also check Amsterdam and Brussels. It would be easier to catch a train from Brussels.

Yes, some flights from SFO are almost double to one place vs. the other. Frankfurt direct is always the most expensive, and it's the one I like to fly into the most. I like the "mini-vacation" in London idea!

Before you book for that overnight + train or plane tickets do the math. Sometimes a substantial amount of your airfare savings will disappear when you include hotel, meals, ground transportation, train or plane, etc.

My airfare savings were almost $1,000. There are lots of reasons for this to happen.

I paid $460 for a sale fare to London. Paris wasn't included.

Just wondering if the airfare (Paris vs London) offering were from the same air carrier or if the London Gatwick offering was offered by a "low cost" carrier?

Please provide more precise details on what airlines are involved and the dates of travel. I'd also be interested in what on-line search functions you are using to find this unusual disparity.
Let's keep in mind that the tunnel to France can be costly if not booked long in advance, the challenges of London transport, and the amount of time you will lose (at least half a day going and a full day returning, since you will need to be in London the night before the trans-Atlantic flight to be sure you get to your plane on time.)

You really expect us to provide evidence for your evaluation.

Bizarre.

And my $49 airfares from LHR To CDG were on AirFrance and British Airways