This paper is an overview of developments and results regarding neutron noise measurements in current mode at the CROCUS zero power facility. Neutron noise measurements offer a noninvasive method to determine kinetic reactor parameters such as the prompt decay constant at criticality alpha = beta(eff)/Lambda, the effective delayed neutron fraction beta(eff), and the mean generation time Lambda for nuclear databases and code validation efforts. A newly developed current mode detection system using two fission chambers in the core reflector was used to accurately measure the kinetic parameters of CROCUS. Characteristics of the system and the performed noise measurements are presented. We implemented noise postprocessing of the current signals acquired at 900 mW using the autopower spectral density/cross-power spectral density (CPSD) method. The final CPSD estimated values were found to be alpha = (153.3 +/- 8.6) s(-1), beta(eff) = (778 +/- 14) pcm, and Lambda = (50.7 +/- 2.9) mu s. In order to comply with experimental uncertainty targets (<3%), the measurement time was 6 h. In comparison with code predictions using MCNP5-v1.6 employing the JEFF 3.1 and ENDF/B-7.1 cross-sectional libraries, we found differences up to 3%, confirming the need for accurate kinetic parameter measurements. In the future, the new measurement system will also be used for studies of spatial and external reactor noise.