For ensuring sustainable nuclear energy, France has chosen to develop sodium cooled fast reactors. The ASTRID project is a demonstrator of such technology exhibiting innovative features such as the CFV core which has a negative sodium void reactivity effect. In order to study in details the uncertainty associated to this parameter, we split it into two components : the central component (CC) which is a positive reactivity effect due to spectrum changes and the leakage component (LC) which is a negative reactivity effect due to the increase of the neutron mean free path. This paper presents the development of an innovative GPT procedure for computing sensitivities of the CC and the LC. With such sensitivities and the use of the COMAC-V2 covariance matrix, we are able to calculate the uncertainties due to nuclear data on each component using JEFF-3.2 nuclear data. The application of the method to the ASTRID CFV core shows a 2.44% uncertainty on the CC, a 2.98percent uncertainty on the LC and a 14.8percent on the total sodium void reactivity effect. There is a correlation factor of -0.5776 between the LC and CC uncertainties. This approach gives perspectives in studying experimental programmes performed in zero power facilities such as MASURCA.