Distortion is necessary, and I’m not optimistic about the results. Why? Look at the legs. The forward leg is longer than the rear leg. If you flop the image on the X axis, the forward leg is still longer. Connect the forward feet (original + reflected) and the rear feet are way too far apart. The problem lies in the fact that onscreen, the Y-positions of the feet are different. The fact that they’re both touching the same floor is irrelevant.
Why do we think reflecting in post would work? Because we’re imagining footage shot directly from the side, where there’s no difference in the Y-position of both feet. Now that would work. Technically, it would only be dead accurate if the camera were at floor level, but that would be picky.
All that said, try Distort>Transform and skewing. You might try the Puppet tool.
Personally, I’d convince the client to lose the effect. But if you said you could do it, you have to bite the bullet and make it work, or lose face.