There has been a growing body of evidence investigating the potential links between the processing of language and rhythm. Recent studies suggest that priming with a rhythmically regular structure, compared to an irregular one, facilitates syntax processing across various populations (Przybylski et al., 2013; Kotz & Günter, 2015; Bedoin et al., 2016; Chern et al., 2018; Canette et al., 2020bé Canette et al., 2019). We hypothesize of the existence of a cognitive system that is responsible for the encoding of hierarchical structure and that is recruited by both rhythm and language (syntax) processing. This study aims to test this hypothesis by examining whether a rhythmically regular structure has a beneficiary effect on the syntactic processing of semi-artificial Jabberwocky language in a population of 41 healthy native French speaking adults. Participants listened to 32 seconds of either rhythmically regular, silent, or rhythmically irregular primes prior to performing a grammaticality judgment task on auditorily presented sentences. We predicted improved accuracy on the grammaticality judgments following exposure to the rhythmically regular prime, compared to the irregular one. Additional rhythmic tasks were conducted to examine whether there exists a relationship between the processing of hierarchical structures in language (syntax) and rhythm and to examine if there is a relationship between sensitivity to the regularity of the stimulus rhythm and rhythmic abilities that involve hierarchical processing. Results revealed a significant priming effect in the regular priming condition, compared to the irregular one, on accuracy across the first three Jabberwocky sentences following the prime. A significant positive correlation was also observed between the task that examines rhythmic abilities and the syntax processing grammaticality judgment task. These findings indicate a short-lived priming effect on Jabberwocky materials, implying that structure building may be weaker in Jabberwocky materials compared to what is observed in the literature for natural language stimuli.