The current study examines the hypothesis that differential aphasia may be due to a problem with language control rather than with language-specific impairment and how this is related to non-linguistic cognitive control abilities. To this end, we report a case study of an L2 dominant French-English bilingual aphasia patient with larger impairments in French than in English. We assessed cross-language interactions using cognates in three lexical decision (LD) tasks, and non-linguistic cognitive control with a flanker task. We also examined functional connectivity between brain regions crucial for language control and language processing. We observed the preservation of cognate effects in a generalized lexical decision task requiring little language control, which indicates intact functionality (and cross-lingual interactivity) of lexical representations. On the other hand, we found diminished linguistic as well as non-linguistic control abilities, suggesting a domain general control impairment. Resting-state functional Magnetic Resonance Imaging (rs-fMRI) analysis revealed altered connectivity between the patient's language control and processing network, consistent with the behavioral data. Altogether, these results are in line with the hypothesis that differential aphasia may originate from general cognitive control difficulties.