I must say I share D@n's opinion here.
What I would do is
start with a plain serial port. Create a dumb (non-clocked) FPGA design that routes the FTDI chip's UART pins to some GPIOs, and hook up the GPS module. Alternatively, use a standalone FTDI-to-UART module or equivalent.
Fire up teraterm (e.g.) on the PC, open the COM port, set the correct baud rate.
Check that the GPS module responds as expected.
Check that the message format is exactly as you expect it.
I suspect this assumption
>> it seems, that the given functions from digilents pmodgps.h heather are doing already the right stuff
What you're trying reminds me of the old joke about a gynecologist retraining as a car mechanic🙂