Chunnel from Folkestone to Calais

I believe the Eurostar from London makes a stop in Calais (i.e., can be booked London-Calais). It doesn't look like Folkestone is on the route, though.

No If you wanted to stop in Folkestone then this is not possible without changes.

To go from London to Calais, you could take the Eurostar to Lille and then transfer to a train to Calais.

To stop in Folkestone you could take the following:

London-Folkstone
Folkstone to Ebbsfleet
Ebbsfleet to Calais.

Or

London to Folkestone
Folkestone to Dover
Dover to Calais (Ferry)

Oh, and nobody calls it the "chunnel."

I think it's useful to explain what you are trying to achieve? Is it that you want to take a passenger train London to Paris? but stopping off to 'see' Folkestone? I suspect not but really not clear. Is there a car involved at all? (The Chunnel is what the euro tunnel is sometimes referred to- the one where you drive you car onto a freight train to get you over the other side)

I also ask the question: What are you trying to achieve here? Do you actually want to visit Folkestone and Calais?

There are lots of trains from London to Folkestone, but none from Folkestone through the Channel Tunnel.
The entrance to the Channel Tunnel is just before Folkestone, the trains do not actually go through Folkestone. The nearest stop is Ashford, some distance before Folkestone, but very few Channel Tunnel trains stop there.
Again, very few Channel Tunnel trains stop at Calais (like 3 per day). And they don't stop at the main station in Calais, they stop at Calais Fréthun, which is in a field outside Calais.

The passenger trains that go through the Channel Tunnel are called "Eurostar", the official timetable is here: https://content-static.eurostar.com/documents/UK_timetable.pdf

If you want to pick up a rented car in France, the best place to do this is Lille (see timetable).
If you are thinking or returning a British rented car, the best places to do this are Ashford or Ebbsfleet (see timetable).

P.S. If you are trying to take a car from the UK the France, the car-carrying trains DO run between the two ends of the tunnel outside Folkestone and Calais. But only between Folkestone and Calais, they DO NOT run from London.
See here: https://www.eurotunnel.com/uk/home/