There is no other noisy device in the vicinity but I moved the system to another room - quiet office with no AC power line in the immediate vicinity - to see if there would be any difference: the noise was still there (!).
I also tried to switch to RSE and NRSE inputs but I got either no signal or something that seemed completely decorrelated with the expected the sensor output.
Also, all the wires are shielded and the multi-wire cable connected to the sensor is about 3 feet long. I moved it around while acquiring the signal with Labview but I couldn't see any correlation between the noise occurences and the wire movements... I don't know if it helps but the kind of noise I get looks also occasionally like this:

This looks really weird to me. I'm under the impression that the problem might come from the SC-board, the DAQ card or the laptop because whenever I measure the force signal with an oscilloscope using the same wiring and under the same conditions, I get no such spikes.
Thibault.