I have 2 BME280 sensors and I remember having some trouble as well. I'm using the exact same sensors as in your picture btw.
Currently they are working, I'm using:
#include <Bme280.h>
Bme280TwoWire bme1;
Bme280TwoWire bme2;
// in setup:
bme1.begin(Bme280TwoWireAddress::Primary);
bme2.begin(Bme280TwoWireAddress::Secondary);
I ended up with this library for my Arduino Giga, the other one didn't work. Hope this helps!