Goat milk somatic cell counts have been collected for several years in France by the national milk recording organization. Information is used for health management, because repeatedly elevated somatic cell counts are a good indirect predictor of intramammary infection. Genetic parameters were estimated for 67,882 and 49,709 primiparous goats of the dairy Alpine and Saanen breeds, respectively, with complete information for milk somatic cell counts and milk production traits. About 40% of the goats had additional information for 11 udder type traits scored by official classifiers of the breeders’ association CAPGENES. Estimates were obtained by REML with an animal model. The studied trait was lactation somatic cell score (LSCS), the weighted mean of somatic cell score (log-transformed SCC) adjusted for lactation stage. Heritability of LSCS was 0.20 and 0.24 in the Alpine and Saanen breeds, respectively. Relationships with milk production and udder type traits were additionally estimated by using multitrait analyses. Heritability estimates in first lactation ranged from 0.30 to 0.35 for lactation milk, fat, and protein yields; from 0.60 to 0.67 for fat and protein contents; and from 0.22 to 0.50 for udder type traits. Genetic correlations of somatic cell score with milk production traits were generally low, ranging from −0.13 to 0.12. Slightly more negative correlations were estimated for fat content: −0.18 and −0.20 in Saanen and Alpine breeds, respectively. Lactation somatic cell score was genetically correlated with udder floor position (rg=−0.24 and −0.19 in the Alpine and Saanen breeds, respectively), and, in Saanen, teat length, teat width, and teat form (rg=0.29, 0.34 and −0.27, respectively). These results suggest that a reduction in somatic cell count can be achieved by selection while still improving milk production and udder type and teat traits.