The Due has the wrong pullup resistors on the board. They are 1k5 and sometimes 1k, but they should be 10k or no pullup resistors.
Sparkfun has 2k2 pullup resistors on the module, it should be 10k.
The sink current for SDA may not be above 3mA.
3.3V / 1k5 + 3.3V / 2k2 = 3.7 mA
A sensor needs to be powered by the Arduino board.
Use the GND and 3.3V from the Due for the sensor, and don't use those wires for something else. Only for one or more sensors.