Short answer, Yes. The floor pans from a Mustang will fit our Cougars. Mustangs and Cougars are brothers under the skin. Their entire framework is the same for both from the front radiator support all the way back to the rear spring's front eyebolt.
I see a couple of the Mustang vendors are finally reproducing floor pans for the 71-73s. The earlier pans will work, its just that the reinforcing ribs/drain channels are wrong for the later cars. The problem is that they moved the front frame rails outboard a bit for the bigger 71-73s and the ribs/channels from the early pans run into the frame rails. You simply had to beat the pans flat in that area so they would fit flat to the frame rails. No biggie, just looked like crap.
Best to use a MIG welder to weld in the new pans, although I've had sucess with gas weld and brazing.
I just put in a drivers side floor pan in a 73 Mustang and I used a "correct" 71-73 pan from Mustangs Unlimited and have to say that it fit really well.
I would suggest getting a spot weld cutter from Eastwood as I plan to do for future jobs as the air chisel isnt the best for removing the seat support panel and no one seems to make new ones for the 71-73's , so you want to not destroy it when removing it. Also no one makes the under the rear seat panel that fits the 71-73's so I had to make a repair panel from scratch for it.
I belive the extra couple dollars for the correct 71-73 floor pan is money well spent. mm