I sent my items to the Birmingham assay office for marking, I still do as Im in Portugal now where the bureaucracy is even worse but the sun shines more lol.
https://theassayoffice.co.uk
You have to contact them and have your own mark set up but they are extremely helpful and can explain everything if you give them a call.
However Im not sure what will happen when Brexit goes through with regard to potentially being charged customs fees on items coming back into France from the UK.
Realistically you may be better getting it done in France but I didn't get far enough through the red tape to know how thats all done Im afraid.
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