Heathrow to Eurostar

Looks awfully tight to me. I wouldn't try it, but others may have different opinions. It would give me horrible anxiety, but some people are not as risk averse.

I also think it is a little bit optimistic. Adding another hour would be better if it was my choice. Also remember you will need the new permit to travel Thru England.

The Piccadilly Line takes an hour, not 30 minutes to St Pancras.

75 minute minimum check in time to Eurostar, so 1415 latest. -
https://www.eurostar.com/uk-en/travel-info/your-trip/check-in

It's not giving much room at all for a late running flight, or issues at immigration or any problems on the tube line. If everything runs well it works, but that is a giant 'if'

Simple answer; no

I don't have an issue going from LHR into London and getting a UK train and expect to be able to accomplish that in 2 hours. But if I - I, me - were considering Eurostar and landing at LHR at noon, I would book a room for the night near St Pancras and then book the Eurostar journey for the next day. Get a good night sleep have a good breakfast and then leisurely walk over to the train station for the check in time.

It's possible, but as others have said, you're underestimating times quites significantly, and it doesn't allow any leeway for flight delays or ground problems.

From touchdown to getting the tube at Heathrow, allow an hour or so on average (could be slightly better or worse):
-15 mins from touchdown to disembarkation (ie taxi to gate, get off aircraft)
-15 mins to walk from gate to passport control
-5-10 mins at passport control (egates)
-15 mins waiting for checked luggage, if you have it
-15 mins walk to tube station
-5 mins waiting for tube

Then an hour to St Pancras from Heathrow by tube. Allow five minutes at least to walk from the tube station to the mainline station, and you need to be there 75 minutes prior to departure to allow time for security and French passport control.

Is there a good reason why you're not just flying directly to Paris?

Don't forget you'll need a UK ETIAS as well.

Is there a good reason why you're not just flying directly to Paris?

A good reason? What amounts to a good reason and is one truly necessary?

Don't forget you'll need a UK ETIAS as well.

no, that doesn't exist yet (and will be for the Schengen Area not the UK).

It is an ETA that is needed, and use the official app or website to avoid unnecessary fees and scams.

I have read all your comments and moved my departure time out to 16:00. I also have a Premier ticket which lets you board later than the usual 90 minutes recommended Eurostar Standard ticket. I have about 5 hours now. That should be enough.

Recommended checkin time for a standard ticket is 75 minutes. But yes, sounds like you now have time.

Given that Eurostar is annoying as flying, but slower, I would just fly to Paris from Heathrow. Really. Will get you to Paris hours earlier.

Plan an alternative way to St. Pancras. Why? On some Sundays, the Piccadilly line doesn't run due to engineering works. Or a delay.

This way, if the Piccadilly line is out of commission, you won't have to start figuring out what to do. You'll have the plan already set.

You will also need to do the EES process (not ETIAS) at St Pancras

My alternate is Heathrow Express to Paddington. Paddington to St. Pancras. I have done this before. I just wanted to try the Piccadilly line. I have read about the upgrades they are doing to accommodate the new trains coming to the Picadilly line in 2026. It is not clear weather they shut down the entire line or you just cannot exit the stations being modified. I will play that by ear I guess.

Instead of the Heathrow Express, your other option is the Elizabeth Line to Farringdon and then either the Metropolitan Line/Circle Line/Hammersmith and City Line one stop to Kings Cross/St. Pancras.

or from Farringdon to St Pancras, then walk across the street. Elizabeth Line and Thameslink are both main line trains, not tubes, so if you have any Railcard discounts the entire trip would be on trains.

Please understand that the Piccadilly route is an hour, not 30 minutes.

The Piccadilly line is having various night and full weekend line closures to prepare for and test the new trains.

Another route is the Heathrow Express to Paddington then a taxi.

And you get Railcard discounts on Heathrow Express, if applicable. A Heathrow Express Early Bird Ticket at £10 plus a tube fare is also cheaper than the Elizabeth Line, although counting pennies is the last thing you should be doing in a situation where speed is of the essence,

Without knowing a date we don't know whether the Piccadilly line, Heathrow Express, Thameslink or the tube lines from Paddington to Kings Cross St Pancras will have a closure on the relevant Sunday.
It's all very well giving alternative routes, but not much use if closed on your travel day.
The Elizabeth Line is only about 10 minutes faster than the Piccadilly line, and less frequent. In theory Heathrow Express then tube/taxi is the fastest route but probably only by about 5 minutes or so over the Elizabeth Line, maybe 10 minutes on the overall journey on a really good day.
The new Piccadilly trains are not currently expected to be in full fleet service before the second half of 2026.