Right, so if you are arriving at 7am on Friday you will have been flying overnight and very tired even if you are one of (OK 2 of) the very few who have no symptoms of jetlag. 3 hours after touchdown you will arrive at your hotel to drop your bags, assuming your room isn't ready at 10am and throw some water on your face. Another hour and you can start your first activity.
Looks like half of Friday and all of Saturday to try to get to terms - while jetlagged - with one of the most impressive cities on this earth.
Up first thing on Sunday and off to Paris for a flying visit, and back to London same day. Better be at the Eurostar check in at St Pancras International bright and early.
The first Eurostar on a weekday gets you to Paris reasonably early but not on a Sunday. The first train on a Sunday is not until the 08:19 (UK time), which doesn't get to Paris until 11:47 (Paris time), just in time to have lunch. The last one back is at 21:13 (Paris time) which gets back at 22:39 (UK time) which doesn't give a lot of sleep before your Monday flight.
Is there a reason you can't fly to Ireland from Paris? There should be plenty of budget airlines making the flight.... You'd get a lot more sleep.
Don't forget to be at the Eurostar check in plenty earlier than the 30 minute absolute cut off, in both directions. My current advice is at least an hour, more on peak summer travel days.
I hope that you choose your London hotel location carefully so that you can get to the station and the airport without too much trouble. You will see so little of both cities you have to plan so very carefully.