Following Jakobson and Levi-Strauss famous analysis of Baudelaire’s poem ‘Les Chats’ (‘The Cats’), in the present study we investigated the reading of French poetry from a Neurocognitive Poetics perspective. Our study is exploratory and a first attempt in French, most previous work having been done in either German or English (e.g., Jacobs, 2015a, 2018a, b; Müller et al., 2017; Xue et al., 2019). We varied the presentation mode of the poem Les Chats (verse vs. prose form) and measured the eye movements of our readers to test the hypothesis of an interaction between presentation mode and reading behavior. We specifically focussed on rhyme scheme effects on standard eye movement parameters. Our results replicate those from previous English poetry studies in that there is a specific pattern in poetry reading with longer gaze durations and more rereading in the verse than in the prose format. Moreover, presentation mode also matters for making salient the rhyme scheme. This first study generates interesting hypotheses for further research applying quantitative narrative analysis to French poetry and developing the Neurocognitive Poetics Model of literary reading (NCPM; Jacobs, 2015a) into a cross-linguistic model of poetry reading.