The resonance associated with the Free Core Nutation (FCN) has been widely studied in Very Long Base Interferometry (VLBI) network measurements and in superconducting gravity records, but few experiments have been done with tiltmeters. In this study we use records collected with a pair of about 100 m long hydrostatic silica tiltmeters, orthogonally installed in an abandoned silver mine at Sainte Croix aux Mines (Alsace, in North-Eastern France). Main difficulties in retrieving FCN parameters from tidal analysis arise from the weak amplitude of PSI1 tidal wave (the closest in frequency to the FCN), as well as from the inaccuracy of the available ocean loading correction. Moreover because of the closeness in frequency of the single constituents of the diurnal tidal band, long (>1 year) records are needed for resolving K1, PSI1 and PHI1 waves. Hence we analyze a 10-year dataset of tilt records, hich has preliminarily required a critical review and a relevant editing for making records suitable for tidal analysis and subsequent inversion of the tidal parameters. A Bayesian inversion is used for a preliminary retrieval of the FCN parameters.