Or can I not use a Serial.println in my ISR function?
Serial output uses interrupts. Interrupts are disabled during an ISR.
To overcome the issue, the print() method invokes the same function that the interrupt service routine does, as many times as needed to make room in the buffer. That WILL slow your ISR down. So, while you can (using relative recent versions of the IDE) get away with using Serial.print() in an ISR, you should not be doing that.
If you MUST, print as little as possible in the ISR.
You also need to make SURE that the functions you are calling from the ISR do not use delay() or rely on interrupts being enabled.
Which BME280 library are you using? Adafruit's and Sparkfun's libraries both use interrupts to read from the sensor.