The paper examines the discrimination of lexical stress contrasts in a foreign language from a neural perspective. The aim of the study was to identify the areas associated with word stress processing (in comparison with vowel processing), when listeners of a fixed-stress language have to process stress in a foreign free-stress language. We asked French-speaking participants to process stress and vowel contrasts in Spanish, a foreign language that the participants did not know. Participants performed a discrimination task on Spanish word pairs differing either with respect to word stress (penultimate or final stressed word) or with respect to the final vowel while functional magnetic resonance imaging data was acquired. Behavioral results showed lower accuracy and longer reaction times for discriminating stress contrasts than vowel contrasts. The contrast Stress>Vowel revealed an increased bilateral activation of regions shown to be associated with stress processing (i.e., supplementary motor area, insula, middle/superior temporal gyrus), as well as a stronger involvement of areas related to more domain-general cognitive control functions (i.e., bilateral inferior frontal gyrus). The contrast Vowel>Stress showed an increased activation in regions typically associated with the default mode network (known for decreasing its activity during attentionally more demanding tasks). When processing Spanish stress contrasts as compared to processing vowel contrasts, native listeners of French activated to a higher degree anterior networks including regions related to cognitive control. They also show a decrease in regions related to the default mode network. These findings, together with the behavioral results, reflect the higher cognitive demand, and therefore, the larger difficulties, for French-speaking listeners during stress processing as compared to vowel processing.