Left hemisphere (LH) strokes often disrupt the language network (LN), causing aphasia. The right hemisphere (RH) has been proposed to contribute to post-stroke aphasia outcomes, but existing findings on RH functional connectivity (FC) changes after LH stroke are inconsistent. This study systematically investigates whether and how the RH FC differs in chronic stroke survivors compared to healthy controls, and whether these differences relate to lesion characteristics and language outcomes. Using a naturalistic movie-watching fMRI paradigm, we compared the RH FC in a large sample of chronic LH stroke survivors (n = 85) to neurologically healthy controls (n = 71). We first used a validated semantic decision fMRI task to identify a core LN and a non-canonical LN (labeled Semantic Network (SN)). We then mapped group FC differences within and between these LH networks and their RH homotopes. Compared to controls, stroke survivors had higher overall within-RH FC and lower within-LH and interhemispheric connectivity. These differences were greater with larger lesions. However, few of the RH FC differences were observed within the RH LN. Rather, most changes were between networks and were distributed widely in the RH. Greater RH connectivity was not associated with lesions or reduced FC in homotopic LH regions, although lesions of LH superior and middle temporal gyri were associated with increased FC between RH SN and LN. RH FC was not associated with behavioral outcomes. These findings show that LH lesions lead to increased RH FC, but the pattern of results suggests that these changes may not reflect meaningful functional reorganization that contributes to language function after stroke. TRIAL REGISTRATION: clinicaltrials.gov NCT04991519.