When Fabry-Perot (FP) refractometry is used to assess the refractivity of gases, it has so far been assumed that the Gouy phase is independent of the presence of gas in the cavity. Here we show, by both theory and experiments, that this is only correct for a non-deformable cavity. For a deformable one, the pressure can affect the radius of curvature of the mirrors. This gives the Gouy phase a component that is proportional to gas pressure. Although being a small effect (1.6 nrad/Pa), since it affects the Gouy phase only when the cavity contains gas, it affects the refractivity on a 10−6 level.