Raymond, UK Gov't pensions, that is you were formerly an employee of the UK state are taxed in the UK and there is a process you have to go thru to make sure you are not also taxed in France though as has been posted, you may end up paying some additional tax in France.
Your UK state pension and any other private pensions should be paid gross in the UK and then declared in France, assuming of course you are tax resident here. You have to apply to your pension provider and HMRC to get this done. Subject I expect to time limits, any tax that you have already paid into the UK will be refunded though of course the Impots will tax you from the date you became tax resident in France.
AVCs according to me are Additional Voluntary Contributions that you are paying into your state pension (so you get more when you retire), so I have no idea what these are in your case and why they would be taxed. If you wish please add some more information.
I do know that there is a different procedure when declaring UK Gov't pensions to the French Impots and for that you need professional advice if you do not know how to do it.