I would say don't go to Paris. You have such a limited time in London, it would be best to experience as much as you can there.

Keep Paris for your next European holiday (even if it's a few years away). It's another city that requires a bit a time to see and experience.

As it's your first visit I'd recommend all the touristy stuff as stated above.

What things do you like to do and what would you like to see?