Mine too Stella 
My UK State pension payment day is a Friday. For the last 3 years this has coincided with Thanksgiving weekend in the USA. As a result my pension has not appeared in my French account until the following monday. The American bank holds on to all the pension payments for three days no doubt making a large profit with our money.
Good grief… I’m obviously much older than you… and thus am in the original set-up. This could be one of the advantages of being an antique… 
Me an’ You Both!
My state pension started in 2011. I did not know there are different set ups.
I am a Non-Resident (UK Fiscally Resident) but with a French Bank Account into which my UK State Pension is paid, plus the £100 at Christmas. This all works very well except for UK Winter Fuel Allowance. My wife gets her share every November into her UK Account and I used to get mine into my French Account. Then it all changed in 2015 and after a long exchange of letters my WFA was sorted out and paid. For a couple of years that worked, but now with time on my hands and some long term problems resolved I have had time to check, only to find no WFA paid for 3 or 4 years.
Got through to International Pension Service this morning, very quickly and was informed that the WFA payment system does not recognise French Banks, so no payment. Entitled WFA or share of it must be claimed in November every year, tel. +44(0)191 21 87777 or 0800 731 0469. Funny that was never notified! Also not possible to back claim for missed years!
Good luck.
Sorry mis-type… £10 at Christmas, sorry if I got your hopes up. The £100 is my share of our WFA.
Why not set up an account with Revolut
Its styled as a British bank so no problems having your money transferred there and once in the account, you can easily transfer the sterling to Euro using the app for simplicity. You can also get a euro card to make either contactless payments in Euro or cash (limited) from a hole in the wall. The rate is usually very close (if not spot on) the current exchange rate so a good deal all round.
Send me your mobile number (by DM y clicking on my name and selecting “message”) and I will send you a link to join Revolut via whatsapp.
for example, just now the rate is 1.1170 and Revolut will give you 1.1167 The rate moves up and down constantly as opposed to some Forex companies I know which seem to fix the rate at the start of the day and only move it down if it exposes them to risk (but rarely up!).
Don’t you know that IDS hated anything to do with France. He fiddled the figures for the meteorological data to include French islands in the Caribbean and Indian Ocean and included them with the data for mainland France, the Hexagon, to prove that France was warm in the winter and all
retirees lost their WFP. We don’t get any Christmas bonus either!
My heart bleeds for you that you cannot claim for missed years. You should have done your homework!