Why is this question indicating a Fraunhofer Region rather than Fresnel Region?

This is too big for a comment so I'm putting it in an answer.

From

https://en.wikipedia.org/wiki/Near_and_far_field

the near field is that part of the radiated field that is below distances shorter than the Fraunhofer distance[1] $d_f = 2D^2∕λ$ from the source of the diffracting edge or antenna of longitude or diameter D.

MY ANSWER: If the aperture size $D$ is taken to be infinite (if the aperture is assumed to be the film size) then the diffraction pattern would be from the Fresnel zone--as you say.

Did he also give an aperture size that you did not put in the question?

For Fraunhofer diffraction the angles of the waves at the observation point should be small and the distance should be large with respect to the wavelength. Since the source plane is stated to be "infinitely large" the first condition cannot be met and the solution is not the Fourier transform. Less strictly speaking "infinitely large" probably is intended to mean "ignore edge effects" in which case the answer is the FT.