Levies on bank interest income

For French fiscal residents, all investment income is assessable to the social charges

WE PAY social charges on unearned income (interest on deposits and bonds etc. not taxed in UK). Our tax office insists this is necessary, are they right?

Yes. For French fiscal residents, all investment income is assessable to the social charges in France, irrespective of the country from which it originates, even income which has not suffered income tax in the UK.