GRANDMA (Global Rapid Advanced Network Devoted to the Multi-messenger Addicts) is a network of 25 telescopes of different sizes, including both photometric and spectroscopic facilities. The network aims to coordinate follow-up observations of gravitational-wave (GW) candidate alerts, especially those with large localization uncertainties, to reduce the delay between the initial detection and the optical confirmation. In this paper, we detail GRANDMA's observational performance during Advanced LIGO/Advanced Virgo Observing Run 3 (O3), focusing on the second part of O3; this includes summary statistics pertaining to coverage and possible astrophysical origin of the candidates. To do so, we quantify our observation efficiency in terms of delay between GW candidate trigger time, observations, and the total coverage. Using an optimized and robust coordination system, GRANDMA followed-up about 90 per cent of the GW candidate alerts, that is 49 out of 56 candidates. This led to coverage of over 9000 deg2 during O3. The delay between the GW candidate trigger and the first observation was below 1.5 h for 50 per cent of the alerts. We did not detect any electromagnetic counterparts to the GW candidates during O3, likely due to the very large localization areas (on average thousands of degrees squares) and relatively large distance of the candidates (above 200 Mpc for 60 per cent of binary neutron star, BNS candidates). We derive constraints on potential kilonova properties for two potential BNS coalescences (GW190425 and S200213t), assuming that the events' locations were imaged.