If you are doing detaxe, yes. They need the info for filling out the detaxe form. If you want to buy a second Birkin in another H boutique, perhaps you need to pay by cash and forego tax refund. At least this is what I heard from a friend who was desperate to get as many Birkins as possible in one trip. Hope this helps.
If your purchase is more than $20,000 they will definitely ask you for your ID because they have to fill out paperwork for the authorities, I believe, to prevent money laundering (as it was explained to me!). Not sure in France but in US they did.
I purchased a birkin from George V last year and did not get asked for passport or ID (clemence, not exotic).
Allan - are there credit cards that are specific to Europe? I was just thinking mastercard or Amex because they are so prevalent here in U.S. ... didn't realize there might be some that are european only so they would assume you were part of EU.
Mine was AmEx, come to think of it...