Less than 10 hours maximum transit time from NYC to Corsica could easily be accomplished non-stop using a Gulfstream G-IV SP. (military designations C-20H, G, etc...) Several other 4,000 nm at mach .80 capable airplanes could do the same.
As for the fastest... well... Presuming one had the command horsepower to make it so: An F-15E (two seater) might be a likely choice due to it's long range and high speed capabilities. With only one inflight refueling the E could probably make it within the required time frame. But line up a few tankers along the route and it could make a series of supersonic dashes and refuelings, perhaps reducing the transit time by more than half. But then positioning tanker assets for short notice missions is no simple matter and may require a longer lead-time than that available...
Never mind the super secretly mission capable Blackbirds or Auroras!
I suggest looking up the performance specs for any type you might choose and learning all you can about it by conversing with current or former pilots of the type.
I hope it's a good story!