Last April, right after I got a B in Paris, I travelled down to Nice. Made a stop in Cannes for a day and went to the H boutique there. I was helped by a lovely SA and I immediately inquired about purchasing any B/K/Cs. She went back to the stock room to check and came back saying she had stock available for purchase but as I had JUST gotten a bag offer in Paris, I was not able to buy a B/K. She stated that if I came back in a few months or so, I’d have no problem getting a B/K then. I did not even purchase anything or express interest in any other items... kinda wanted to try my luck!
So they definitely do offer to tourists there without previous spend history!