I recreated your issue: select the foot object, go to edit mode, selct the bottom face you want to be aligned, press Shift S > cursor to selected. Back in object mode right click and choose "Set origin to 3D cursor".
Now you can activate the face snapping otpion, ticking "Align rotation to target", and easily place your objects.
Working on your file I did 4 actions:
enable affect rotate in the face snap options (so that the snapping acts even when manually rotating the object)
Applied scale of your foot object (Ctrl A)
The most important: selecting a foot and pressing Alt G, Alt S, Alt R resets the object's transforms: in its rest position the object has to be in the center of the world (0,0,0), with no rot (0,0,0) and with unity scale (1,1,1).
Untick this transform option that make your object locked on rotations.
In this state your object wasn't straight and centered. The face snap acts on the whole object, based on its origin; you can think the of the origin as a ghost vertex which is parent to all the others vertices. Snapping gives to the origin the loc and rot of the underlying face, and this is reflected to the whole object, if this object is straight vertical in rest position.
So you have to change your object in edit mode so that it fits the requirements (as in photo quad view).
At this point simply move (G) and duplicate (Shift D) with the face snapping option to easily place the feet.