Understanding the turbulent structure of molecular clouds is essential for linking galactic environment to the regulation of star formation. Although Galactic molecular clouds have been studied extensively, extending turbulence-mode analysis beyond the Milky Way remains challenging because of the limited spatial resolution and dynamic range of extragalactic observations. We assess the applicability of the Brunt & Federrath (2014; BF14) framework to molecular clouds in M33. We apply BF14 to 128 ¹³CO(2-1) clouds, selecting a primary quality-controlled sample of 54 clouds and a more restrictive 25-cloud subsample defined using a stricter extraction-padding criterion (PAD=2) for quantitative analysis.Tests of cloud and noise power spectra, Fourier-space cutoffs, extraction padding, and Monte Carlo uncertainties demonstrate that the retained spatial frequencies are dominated by astrophysical signal and that the inferred turbulence-mode fractions are robust against reasonable analysis choices. Both samples yield consistent distributions of the solenoidal fraction, with mean values of R ≃ 0.22 for both samples and median values of R ≃ 0.18 and 0.17, respectively, indicating that compressive motions dominate the turbulent energy budget. No strong systematic variations of R are found with galactocentric distance or tracers of recent star formation. These results demonstrate that, despite the challenging spatial resolution of current extragalactic molecular-line observations, the BF14 framework can be applied reliably to nearby galaxies using spectroscopic observations alone. To our knowledge, this constitutes the first application of the full BF14 formalism to extragalactic molecular-cloud observations.