Yes, you only need TX, RX and ground but are you sure you are using the correct voltages at the interface?
When you say "FTDI module", do you mean ONLY an FTDI interace or is it a full USB serial interface as used for PC serial links. If it is, it may have an on-board RS232 level shifter which will invert the signals and produce wrong voltages for your application.
Even if your FTDI module produces 5V logic levels, you should really use level shifters to and from the lower voltages used by the SIM module.
Brian.