Hemispheric lateralization for language production and its relationships with manual preference and manual preference strength were studied in a sample of 297 subjects, including 153 left-handers (LH). A hemispheric functional lateralization index (HFLI) for language was derived from fMRI acquired during a covert sentence generation task as compared with a covert word list recitation. The multimodal HFLI distribution was optimally modeled using a mixture of 3 and 4 Gaussian functions in right-handers (RH) and LH, respectively. Gaussian function parameters helped to define 3 types of language hemispheric lateralization, namely "Typical" (left hemisphere dominance with clear positive HFLI values, 88% of RH, 78% of LH), "Ambilateral" (no dominant hemisphere with HFLI values close to 0, 12% of RH, 15% of LH) and "Strongly-atypical" (right-hemisphere dominance with clear negative HFLI values, 7% of LH). Concordance between dominant hemispheres for hand and for language did not exceed chance level, and most of the association between handedness and language lateralization was explained by the fact that all Strongly-atypical individuals were left-handed. Similarly, most of the relationship between language lateralization and manual preference strength was explained by the fact that Strongly-atypical individuals exhibited a strong preference for their left hand. These results indicate that concordance of hemispheric dominance for hand and for language occurs barely above the chance level, except in a group of rare individuals (less than 1% in the general population) who exhibit strong right hemisphere dominance for both language and their preferred hand. They call for a revisit of models hypothesizing common determinants for handedness and for language dominance.