James you might be surprised but I guess France is like Italy.
They are obsessed with the quality of milk for the cheese making but the milk you get in stores is nothing but watered down ultra pasteurized cooked garbage. It taste like it has been boiled for ages skimmed and watered down.
They don't know what they're talking about when it comes to milk to drink right away. And I'm talking about fresh milk, the UHT kind doesn't even taste like milk over here.
The best milk I drink is the one I drink in the United States the fresh milk you get in the big jugs..ahhhh

I only get one decent milk over here it is the one from our province's dairy and it is not a case it is sold even in other regions and supply restaurants and cafès throughout northern italy.
I never happened to taste Irish milk but I guess it's similar to what I drink in the States.
Also they never heard of half and half.
About butter you have differences based on making process, some say European butter taste better in my opinion is not so, I tasted far more better butters in America than here, but again in USA you have get a plethora of every kind of butter and brands each one got its own taste over here you just get three brands/kinds..litterally.
Lidl use to sell Irish butter and it's very good.
Looks like they don't give much importance to milk cream and butter but more to milk for cheeses and cheesemaking.