Have you queried the French Embassy in the UK about this?
I thought the 'certificat de demenagement' was only for those moving from somewhere else in France, and is delivered by the municipality where they're moving from.
It could be that out of habit the removal company is asking you for certificate which, as non-French, you don't have to supply.
When we had an international move back to Reunion from South Korea I can't remember being asked for this certificate, but admittedly Korea is not European Union.