You really need something external to both provide the analog inputs for the force sensors and the serial communication for the GPS module.
The simplest "something" is another microcontroller. Ideally one with two UART ports.
You can then:
- Communicate between the microcontroller and the GPS with one UART
- Sample the FSRs with the microcontroller
- Format and send the data to the ESP-01 through the other UART
SoftwareSerial you chould just about do it with an Arduino Uno (though you'd have to disconnect whatever was on the hardware UART every time you wanted to program it), but ideally something with more UARTs would be better, such as a Mega2560.
A halfway house between the two would be a board based around the ATMega32U2 which uses a direct USB connection for programming leaving the hardware UART free to be used permanently. However you'd still need to use
SoftwareSerial to emulate the second UART (maybe best for the GPS since it's then only used for receiving).