Welcome Grace,
If this is your first trip and you havent done some planning, i would do so. As mentioned backtracking isnt good for the pocketbook. Look at your PATH.
just a comment. If you spend your time in the UK first and then go to Paris. Then if you have to go back to the UK to fly out, transportation shoudlnt be an issue since youve "been there done that". but i would try to fly out of paris if its the above plan.
If youve booked your flights already, it could be too late, but check for what fees/charges for changing if any.
also, as mentioned the pro/cons of buying a train ticket in advance. Weight the +/-. are you willing to buy another tickets(s).
On one of my trips my flight to Europe was delayed ~ 2 hours and the connecting was delayed another hour. my previous trip, no hitches on ANY of my flights. My trip last year was hitch free. on my last trip, i booked rooms in AMS (my hub) just in case of a delayted flight. That delayed fight i mentioned cost me 450 USD. I can stay in AMS overnight in a really really nice hotel for 450. So i decided to stay overnight both in/out of AMS. This year, im going to chance it since my connecting flight is 5 hours after im suppose to land. Again, it all depends on how you want to do it and how comfortable you feel about the connections.
happy trails.