It's true that a good guidebook is the place to start.
Of course, you'll have to look at Eurostar schedules and determine how many hours you actually will have from arrival until departure.
Once you know exactly how much time you have to explore Paris, you can begin to prioritize.
My opinion would be that since you have time in London but very limited time in Paris, you see the British Museum instead of the Louvre. To actually enter the Louvre will eat up a chunk of time that you don't have, so just see it from the outside.
Another opinion would be regarding the Eiffel Tower. You can walk past it, admire it from below--but you don't need to ascend. That's another activity that can really eat time because even if you have pre-purchased tix to ascend, there are lines to come back down.
(Remember I said these were opinions--yours may differ! And if you DO want to ascend the Eiffel Tower, go to the official website and buy tickets in advance.)
You'll also need to decide if you want to use a tour bus. You can read about the hop-on-hop off bus companies and the Foxity bus tour:
tripadvisor.com/ShowTopic-g187147-i14-k41865…
There's also the Sandeman's walking tour:
newparistours.com/daily-tours/paris-free-tou…