Not an 8.8. They came out later. Depending on the size of the motor it could be an 8", a basic 9", or possibly a 9" with the stronger 31 spline axles. Can you take a picture of the carrier housing from the front? If it has a tag, you can clean it off and get both the ring size and ratio. I think the early 60s 8" axle housings had a step down in OD size 6 or 8 inches from the brake backing plate. Don't recall ever seeing a 9" axle with this step.
Since the 260 was the top dog engine in the 63 Falcon lineup I don't think any Falcon from that year ever had a 9" from the factory.
No 9" in a Falcon! If it has a bolted cover on the back and 4 lug nuts it is 7 1/4" or 6 3/4" , I am not sure of the exact ring gear size. If the carrier comes out from the front it is most likely an 8" The 8" removable carrier is square looking as opposed to the 9" being more rounded.