But except if there's an interest in using the gyroscope, IMHO it's a bit of an overkill, while a LIS3DH will use 50-100 times less current for free fall detection (between 6 and 11µA), ADXL345 over 10 times less (40µA)
I agree with this also especially due to the low current consumption. I would not go as far as dismissing something as overkill when considering the intended usage though.
I don't have experience with free fall detection systems but somehow it sounds more suitable for detecting a direct gravitational falling and not a person falling which likely involves legs slowing down and the fall starting from the person already standing on the ground. But I am definitely interested in hearing how this works out as this is one of those rare projects that isn't just a "nice to have". Great idea!