Assertion: In YDSE, if a thin film is introduced in front of the upper slit, then the fringe pattern shifts in the downward direction.

Reason: In YDSE if the slit widths are unequal, the minima will be completely dark.

If a film is introduced in upper slit, the optical path traveled by ray from upper source is more and that traveled by that from lower source, hence some finite path difference exists at the point of earlier central maxima(point equidistant from both sources). Now to compensate for this extra path difference, ray from upper source needs to travel lesser than ray from lower source. So the central maxima would now be obtained at a point of screen that is closer to the upper source. Hence central maxima shifts upwards, so does the pattern.
If slit widths are different, intensity of light from both the sources is different.

$\text{So the minima will have intensity}{(\sqrt{{\mathrm{I}}_1}-\sqrt{{\mathrm{I}}_2})}^2>0\text{.}$

So the minima would not be dark. 
Therefore both the assertion and reason are incorrect