The UK funds your health costs IF you have an S1. It pays the exact equivalent of what the French health system would reimburse in the same circumstances if you didn’t have an S1 and so your costs were funded by France. In most cases this is around 70% of the total cost of treatment.
If you’re retired with a UK state pension then presumably you do have an S1. That being the case, the answer to the above question would be Yes, the UK pays the reimbursable part of you healthcare costs.
It depends entirely on what cover you chose.
Your policy will tell you exactly what it covers, but if you went for low-level cover, you would expect to be asked to pay more than if you’d gone for a bells and whistles policy with higher monthly premiums.
Hope this helps.