A sleeping STM32 can be woken up by a rising edge on its wake up pin. But if the IC on the other end of the line only interrupts as falling edge, is it possible to invert it somehow ?
Yes, the WKUP pin works like that. If you really need standby state, you pretty much have no other choice left to wake up the device. You can, however, put a simple inverting transistor in front the the WKUP pin like this:
Check the data sheet, you might be able to spare R2 if a proper pull-down resistor can be switched on for WKUP inside the chip.