* A C4 transmission designed for a 1961 Falcon (or a very close year): The C4 changed slightly over the years, so compatibility is crucial.
* A C4 bellhousing that matches your Falcon's engine: This is essential for proper mating to the engine.
* A driveshaft shortened to the correct length: The driveshaft from the manual transmission will be too long for the C4. This often requires a custom driveshaft.
* A transmission crossmember designed for a C4: The stock crossmember won't work.
* A torque converter: Automatic transmissions require a torque converter.
* Possibly a modified or replacement floor pan: Depending on the specifics of the C4 and your car, the transmission tunnel might need modification to accommodate the larger automatic transmission.
* Shift linkage or cable (and possibly the associated parts and modifications): The shifter for the C4 will be different.
* Possibly additional wiring: If you need to wire in a transmission-related component.
The process is a major undertaking requiring mechanical skills, specialized tools, and a good understanding of automotive systems. It's not a simple bolt-on swap. It's far easier and cheaper to find a suitable 3-speed manual transmission if you want to stay with a manual. If you are determined to go automatic, seek the assistance of an experienced mechanic.