The formation of protoplanetary disks is not well understood. To understand how and when these disks are formed, it is crucial to characterize the kinematics of the youngest protostars at a high angular resolution. Here we study a sample of 16 Class 0 protostars to measure their rotation profile at scales from 50 to 500 au and search for Keplerian rotation. We used high-angular-resolution line observations obtained with the Plateau de Bure Interferometer as part of the CALYPSO large program. From ¹³CO (J = 2−1), C¹⁸O (J = 2−1) and SO (N_j = 5₆−4₅) moment maps, we find that seven sources show rotation about the jet axis at a few hundred au scales: SerpS-MM18, L1448-C, L1448-NB, L1527, NGC 1333-IRAS 2A, NGC 1333-IRAS 4B, and SVS13-B. We analyzed the kinematics of these sources in the uv plane to derive the rotation profiles down to 50 au scales. We find evidence for Keplerian rotation in only two sources, L1527 and L1448-C. Overall, this suggests that Keplerian disks larger than 50 au are uncommon around Class 0 protostars. However, in some of the sources, the line emission could be optically thick and dominated by the envelope emission. Due to the optical thickness of these envelopes, some of the disks could have remained undetected in our observations.