STM32F0 - run user program from SPI flash memory
The bad news is no, you can't execute directly from SPI flash. You could store some of your program on the external flash, and copy it to RAM a bit at a time for execution, it would work, but it's a terrible idea overall. It's probably easier to change to a more suitable microcontroller.

The stm32f070f6p6 is a similar part with 32k instead of 16k of flash, it may even be pin compatible.