French term (edited): compl�ment de prix

I'd merely suggest you beware of "supplement" if the French is "complement", since they are not the same thing!

A supplement is over and above (the agreed price, etc.).
A complement is an agreed part of (the agreed price, etc.)

So if your dairy farmer sells 1000 gallons of milk, he might get X euros per gallon for 900 gallons of milk of an agreed quality, plus a complement of X euros per gallon for 100 gallons of high-quality cream, say, both at the factory gate, the whole making X euros per gallon of milk at the farm gate. IOW, the extra quality is factored into what is regarded as the "price".

If regarded as a supplement, that X euros per gallon at the farm gate would become the same "X euros" PLUS extra for extra quality, say.

It probably makes no real difference, but I can simply imagine the CAP arguments if British dairy farmers start thinking their French counterparts get paid a "price", which will have its equivalent(s) in the British Isles, PLUS a SUPPLEMENT, when "all they get" is the "price", comprising a COMPLEMENT.