Don't know for sure about the Cougars, but the earlier Ford (60's Galaxies etc) with floor shifts had a special shift arm for the floor shift models that had the shift arm pointing up instead of down. If you attempt to hook it up with with the trans arm pointed down instead of up it will reverse the shift pattern (in other words park will be where low is).

Some of the mounting kits for aftermarket shifters have a special arm that bolts to the original column shift arm on the tranny that points in the proper direction. and gives you a couple of different mounting holes to obtain the proper throw.