When I tried to get foreign currency - just Canadian dollars - in my US hometown, it was very difficult. What source are you thinking of when you say this would be by far the easiest.

OP, I wouldn't recommend dollars to pounds to euros in LHR - 2 conversions is twice as bad. I haven't researched, but I would bet there's an ATM in the Nice airport - that's where I'd start.

I agree with the others - use a credit card without foreign fees as much as possible, with ATM cash only for what's needed. If you truly need 1000 euros on arrival for some reason, I'm guessing ATMs won't give you that much, so you may be stuck with one of the less attractive alternatives. ATM's might let you take 1000 out over 3 days, if that's possible.

Be sure to tell your bank/cc company that you'll be overseas. A max withdrawal on consecitive days may raise a flag without advance notice.