The observation of acoustic phonons located at the surface of uncoated fibres or guided in thin films deposited on fibres by Brillouin light scattering spectroscopy (BLS) is reported. The BLS technique is non-destructive and non-intrusive and is well applicable to non-planar sample geometries. Investigations were carried out on bundles of commercially available carbon fibres, in which a single fibre was 5 microm in diameter. With regard to the detected surface acoustic excitations, each fibre can be considered as an infinite halfspace owing to the large ratio of fibre diameter to wavelength. The shear modulus, which is highly relevant for the intended technical application, was determined by measurement of the Rayleigh mode phase velocity of the uncoated fibres. These fibre bundles were coated with boron nitride (BN) in a continuously driven thermal chemical vapour deposition (CVD) process using trimethyl borate and ammonia as precursors. In comparison to carbon, BN is expected to improve the mechanical properties of fibre-reinforced composites such as fracture toughness at high temperatures. The measured velocity dispersion of the Rayleigh mode of this film-on-substrate system permitted the comparison of the shear stiffness of the carbon fibre and of the BN film material. The results evidence the desired effect of a distinct stiffness reduction of the coated fibre relative to the uncoated fibre in the near-surface region. Additional information can be obtained on the homogeneity of the deposition across the whole fibre bundle.