The Ministry interpretation is quite correct. Cost sharing is not "remuneration" which is defined in the Oxford English Dictionary as "Reward, pay for services rendered"
English is a very complex and subtle language and VERY careful translation is needed to get meaning correct in legal terms. Brussels is not very good at that. Because French has a small vocabulary compared to English they often choose an inappropriate translation and it's necessary to understand the intention of the rule makers, who then turn out not to have thought through their own intentions!
When flying an aircraft where more than one state is involved e.g D reg in French airspace it's generally the rule of thumb that more onerous or restrictive of the two sets of rules will apply.