Is there an overnight train in the Eurostar's schecule from Paris to London?

No. The last one of the day leaves Paris at 8:43 p.m., arriving in London 10:28 p.m.

You can;t have an overnight train on that route - the trip is much too short. Unless you just want to take the last train and then sleep in the RR station in paris.

there is one overnight Eurostar train but it doesn't go into Paris but runs from London to the French Alps, arriving in the morning. Returns however are done late in the dat.

sorta hard to overnight on a route that takes less than 3 hours.

(yes, I know there is a night train London/Edinburgh - a route that normally takes about 4 1/2 hours. But that's another story)

There were plans to have longer-distance sleeper trains that takes the Channel Tunnel. Some of the sleeper cars were already built before they cancelled the services.

The equipment, finished and unfinished, had been modified and sold to VIA Canada for service in the Windor-Quebec corridor, as well as the "Ocean" to Halifax.