Cheap flight to London/Paris

Not much competition in Atlanta. That may be the best you can do.

You can fly to Orlando from $204-$214 round trip. Norwegian Air Shuttle flies to London Gatwick and home from Paris in October for $213.90 and as low as $287.90 respectively. That's about $700.
I'd hang back and watch the budget airlines, consolidators and air discounters. Who knows what the Coronavirus is going to do for supply and demand of the airline business. Better airfares could be in the future--or not.

We are watching flights as well from Tampa, Orlando , or Miami to London.

I see $964 from and back to Atlanta for random dates in October booked on British Airways. The outbound is on BA and the return is on American with one stop on the way. Those are Economy Basic class: no checked bags.

You can set up Google Flight alerts and track the prices on several dates and locations. Once you have determined a good price, buy from the airline directly.
Many OP's here will warn you about buying airline tickets from third party vendors, because if the flight gets canceled, you will have to deal with the third party vendor, not the airline.
Good luck and safe travels!

Are you trying to get directly to Paris upon arriving in London, or spending a few days sightseeing in London and then going to Paris?

If the latter, then it is much easier to take the Eurostar train from London to Paris.

(I think I may have misunderstood, i think you are only talking about the “external” flights e.g. ATL —> London and Paris —> ATL)

"I'd hang back and watch the budget airlines, consolidators and air discounters." You are in for a world of hurt if anything goes wrong. Book directly with an airline. Repeat this after me, "I will book directly with an Airline." :)

Just make sure you are looking at "multi city" tickets - Atlanta to London and Paris to Atlanta, all on one ticket. Don't look at two one-way tickets - that's potentially much more expensive.

This year, air fares to Europe seem to be much higher than I was expecting - and I'm in New York, a more competitive airfare market to Europe than Atlanta is.

As for whether it's too soon or too late, nobody knows. Airlines use computers to adjust fares multiple times a day, depending on tiny fluctuations in supply and demand. The best you can do is watch the fares for a while, book when you find a fare you can live with, and not look back.

As for websites, you can use Google Flights or Kayak. But do be careful about Franken-tickets - those cobbled together from different airlines that aren't in an agreement. Some online agents, like Kiwi, are notorious for selling these, and leaving you in the lurch if there's any problem. If you don't buy direct from the airline, at least make sure you're on a single ticket.

If you're going to go what David proposed (get to Orlando on one carrier, then to Europe on another unconnected carrier), make sure you understand all the risks. Here's a good summary: https://www.tripadvisor.com/Travel-g41707-c207311/Newton:Massachusetts:Connecting.On.Separate.Tickets.html

Forget Expedia! As others have said,always, always book directly with the airlines. If there are any problems with the flights, they will take care of you before those who booked with third parties. Remember the volcano in Iceland that disrupted all flights to and from Europe from US? Passengers were stranded but those helped first booked with airline direcrly.
For a search engine I use Google/ flights.

No search site shows all flights, but in my unscientific experience the fullest is matrix.itasoftware.com
It's owned by Google but doesn't sell tickets like Google Flights, maybe why it has more info.

Atlanta is a major gateway, one of the busiest airports in the USA, so I would assume sees plenty of trans-Atlantic flights.

Flight prices are conjured up by the mystical computer algorithms along with AI. They can change prices on the same flight several times a day. That's as tough as roulette. So set yourself a target, buy if it comes up, and then stop reading, for fear of buyer's remorse. And do buy from the originating airline rather than an an on-line agency.

I've never know Google Flights to sell tickets. It just connects you to the appropriate airline (or I guess third-party seller) so you can purchase. I've often been shown multiple potential sources (partner airlines) for the same ticket, sometimes at different prices. I just look at the prices and go directly to the website of my choice.