This is an acoustic and articulatory study of Canadian French rhotic vowels, i.e., mid front rounded vowels /ø œ̃ œ/ produced with a rhotic perceptual quality, much like English [ɚ] or [ɹ], leading heureux, commun, and docteur to sound like [ɚʁɚ], [kɔmɚ̃], and [dɔktaɹʁ]. Ultrasound, video, and acoustic data from 23 Canadian French speakers are analyzed using several measures of mid-sagittal tongue contours, showing that the low F3 of rhotic vowels is achieved using bunched and retroflex tongue postures and that the articulatory-acoustic mapping of F1 and F2 are rearranged in systems with rhotic vowels. A subset of speakers' French vowels are compared with their English [ɹ]/[ɚ], revealing that the French vowels are consistently less extreme in low F3 and its articulatory correlates, even for the most rhotic speakers. Polar coordinates are proposed as a replacement for Cartesian coordinates in calculating smoothing spline comparisons of mid-sagittal tongue shapes, because they enable comparisons to be roughly perpendicular to the tongue surface, which is critical for comparisons involving tongue root position but appropriate for all comparisons involving mid-sagittal tongue contours.