Separation of USB and serial communication.
On the Leonardo, the main Serial class refers to the virtual serial driver on the Leonardo for connection to your computer over USB. It's not connected to the physical pins 0 and 1 as it is on the Uno and earlier boards. To use the hardware serial port (pins 0 and 1, RX and TX), use Serial1. (See the Serial reference pages for more information.)
I'd suggest changing the connection to the hardware serial pins, and using Serial1 to read from the GPS, not SoftwareSerial.