Recent evidence suggests that three specific brain networks show state‐dependent levels of synchronization before, during, and after episodes of generalized spike‐wave discharges (GSW) in patients with genetic generalized epilepsy (GGE). Here, we investigate whether synchronization in these networks differs between patients with GGE (n = 13), their unaffected first‐degree relatives (n = 17), and healthy controls (n = 18). All subjects underwent two 10‐minute simultaneous electroencephalographic–functional magnetic resonance imaging (fMRI) recordings without GSW. Whole‐brain data were divided into 90 regions, and blood oxygen level–dependent (BOLD) phase synchrony in a 0.04–0.07‐Hz band was estimated between all pairs of regions. Three networks were defined: (1) the network with highest synchrony during GSW events, (2) a sensorimotor network, and (3) an occipital network. Average synchrony (mean node degree) was inferred across each network over time. Notably, synchrony was significantly higher in the sensorimotor network in patients and in unaffected relatives, compared to controls. There was a trend toward higher synchrony in the GSW network in patients and in unaffected relatives. There was no difference between groups for the occipital network. Our findings provide evidence that elevated fMRI BOLD synchrony in a sensorimotor network is a state‐independent endophenotype of GGE, present in patients in the absence of GSW, and present in unaffected relatives.