Hello DCD. We did have a recent thread on choice of mobile phone (cellphone) network in the UK:

http://www.flyertalk.com/forum/u-k-i...-provider.html

and if you search on this forum for 'SIM Card', you'll get several more.

Pay-as-you-go services are widespread both in the UK and France, so you won't be short of choices. The SIM card is the chip that you insert in your phone to identify it on a GSM network - to use it, you'll need to make sure that your phone is GSM900/1800/1900 compatible.

Using a UK SIM for roaming in France, however, is often expensive. It's getting better, but you'd need to do the sums to see if it's better for you to get another SIM for use in France, depending on your expected usage.

Have a read through the old thread, but I'm sure there are plenty here who can help you if you have any more specific questions.