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Knowing the local variations of the gravity field is a prerequisite for an accurate accelerator alignment in a Euclidean plane, especially for large machines. Within the scope of the Future Circular Collider (FCC), the proposed next-generation particle collider with a circumference of 91 km, efforts are made to compute a local centimetric geoid. Local and global geoid models covering the studied area are not consistent (decimetric differences), so a local solution must be found. To achieve the computation of a centimetric geoid, that will be used for the construction of the tunnel and then refined for the alignment, different methodologies are studied. This paper focuses on the application of the Stokes-Helmert method (Fugro/UNB SHGeo+ package) to compute a local gravimetric geoid. The paper first describes the evaluation of the gravity dataset provided by the BGI (Bureau Gravimétrique International), the IGN (Institut Géographique National) and Swisstopo (Federal Office of Topography). Then the computation of the geoid model is developed, evaluating the influence of lateral rock density variations. Finally, its accuracy is evaluated using a dedicated 40 km geodetic control profile composed of 36 GNSS/levelling stations and 83 deflections of the vertical observations.