The conformal coating of a 50 nm-thick layer of copper nanoparticles deposited with pulse chemical vapor deposition of a copper (I) guanidinate precursor on the cladding of a single mode optical fiber was monitored by using a tilted fiber Bragg grating (TFBG) photo-inscribed in the fiber core. The pulse-per-pulse growth of the copper nanoparticles is readily obtained from the position and amplitudes of resonances in the reflection spectrum of the grating. In particular, we confirm that the real part of the effective complex permittivity of the deposited nano-structured copper layer is an order of magnitude larger than that of a bulk copper film at an optical wavelength of 1550 nm. We further observe a transition in the growth behavior from granular to continuous film (as determined from the complex material permittivity) after approximately 20 pulses (corresponding to an effective thickness of 25 nm). Finally, despite the remaining granularity of the film, the final copper-coated optical fiber is shown to support plasmon waves suitable for sensing, even after the growth of a thin oxide layer on the copper surface.