Thanks for your question
You will remain liable to UK tax on this pension as it arises in the UK and falls within the remit of a governmental pension (and then should advise the French tax authorities of this pension and the fact you bring it into France - and also advise them of any tax suffered as you will create a tax consideration as you will be resident in France so do seek some advise on the tax position in France)
So the first £10,600 will be tax free (assuming you are under 65 in age) so tax of £780 a year will arise (and PAYE will continue to operate against this pension payment) but there will be no National Insurance deductions as a pension.
As for NHS entitlement
I have added a link here from the NHS website that advsies on entitlement to NHS free treatment http://www.nhs.uk/chq/pages/1086.aspx?categoryid=68 (we are a UK tax expert forum not NHS!) And there are contact details if you wish to ask further into your position
But any return to the UK will se you entitled fully to NHS services - see link here
Please do let me know if you wish me to expand on any of the information I have provided.
I am sure you can appreciate we are not French tax experts - so do seek expert advise on the French position