It could just be you need more light.
Similar to a still camera, each frame is captured at a particular exposure setting. For a given light intensity, the exposure settings are determined by the aperture (f-stop) and shutter speed (not to be confused with cine rate), and possibly the sensor's "ISO" setting.
Most cameras have an automatic exposure setting that allows the camera to automatically select its own aperture, ISO and shutter speed based on the lighting conditions. Your camera has this capability.
According to the Canon Vixia HF100 User Manual, the automatic exposure is the only choice. It doesn't seem as though it allows you to select any of these exposure settings yourself (you can tweak the overall exposure if you wish, but you cannot select individual aperture, shutter speed or ISO on this particular camera).
What may be happening is that given the low-light conditions, the aperture that the camera selects is at maximum, the shutter speed is pretty slow too. Just like with a still camera, movement will blur the image when slow shutter speeds are used. If that's what's going on here, the solution is to provide more light. That way the camera will select a faster shutter speed for the same exposure at the sensor.
Remember a while ago I mentioned that camera and video accessories can get really expensive, really quickly. This is another reason: lighting.
Typically in the industry, when shooting indoor scenes all the lamps and lights in the house -- ones that make it into the actual scene -- are replaced with rather dim bulbs. The "real" light doesn't come from those household lamps. Instead, the real light comes from very bright lights made especially for cinematography -- these special lighting fixtures don't make it in front of the camera, so the final viewer never sees them. The viewer assumes that the light is coming from the nearby lamp in the scene. But it's really not. Its coming from a really bright light source (or perhaps multiple sources) off to the side and out of view.
As a matter of fact, even outdoor, night scenes are often actually shot during the daytime, sometimes in full sunlight, and then they are made to look like nighttime scenes in post processing, by applying a blue filter. (And there maybe be other filtering tricks involved besides just the blue one.)
So in short, you might wish to try more light, one way or another.