Holy... more than a 1,000 euros per night? That's almost two months worth of salary for me - for 5 nights.
As to your question, the same thing as always applies: if it's very important for you to get the "Intendance Villa" (as a minimum), then you should book that room type (villa type?). While upgrades should happen if there is availability, I guess they don't have too many of these villas so there's a non-zero risk that you would have to make do without having both a jet pool and an infinity pool.
Whether you book on the BT page or the Accor page probably makes less of a difference. If you are worried, e-mail them after placing the reservation to confirm that your Platinum membership is on the booking and maybe hint that you want that upgrade if possible. Then you can always e-mail again a few days before arrival and nudge them again about the upgrade.