Fetal cerebral brain magnetic resonance imaging (MRI) is critical for the detection of abnormal brain development before birth. A key image processing step is the reconstruction of a 3D high resolution volume from the acquired series of 2D slices. Several types of MR se- quences are commonly acquired during a scanning session, but current reconstruction methods consider each sequence (or contrast) separately. Multi-contrast techniques have been proposed but they do not compen- sate for potential movement during the acquisition, which occurs almost systematically in the context of fetal MRI. In this work, we introduce a new method for the joint reconstruction of multiple 3D volumes from different contrasts. Our method combines the redundant and complemen- tary information across several stacks of 2D slices from different acquisi- tion sequences via an implicit neural representation, and includes a slice motion correction module. Our results on both simulations and real data acquired in clinical routine demonstrates the relevance and efficiency of the proposed method.