Here is the screen grab an IR+visible spectrum image via the Sigma DP1 before post-processing a raw capture (X3F file, Sigma-speak for raw). The Foveon sensor captures both the IR and the visible light spectrum when combined with a filter that attenuates the intensity of IR. It took me several trial and errors to find a filter that decreases the intensity of IR and at the same time let the visible spectrum pass through.
Is this "false-color"? I don't know. By convention, "false-color" IR is a term used during post-processing when we adjust the sliders in the Channel Mixer portion of Photoshop. As you can see in the screen grab, the image is a raw file and all sliders are all in neutral setting: