Purpose: In the past three decades, statistical learning, that is, the capacity to detect patterns and regularities in the environment, has been shown to have an important role in language development. In particular, the ability to detect nonadjacent dependencies (NADs) between linguistic elements that are separated by intervening material seems to be linked to morphosyntactic development. However, there are few studies with French-speaking children, and none using artificial language learning methodologies. Method: We investigated the acquisition of NADs in 18-month-old (n = 30) and 27-month-old (n = 32) monolingual French-learning children in an adaptation of Gómez (2002) artificial grammar learning study to a central fixation eye-tracking paradigm. After a 2-min familiarization with three element strings (e.g., /na sok? fib/), we monitored looking times for grammatical versus ungrammatical strings in two blocks of four test trials each, expecting a novelty effect at 18 months and exploring the behavior at 27 months. Results: No significant effect of grammaticality was found at either 18 or 27 months for the overall task. However, at 27 months, we observed a significant decrease in gaze duration for ungrammatical test trials between the first and the second blocks, together with a tendency to look longer at grammatical stimuli in the second block, a pattern of results that, if confirmed in future studies, might indicate the start of novel NAD learning. Conclusions: Given the failure to clearly replicate effects observed in the studies with English-learning children, we propose several theoretical hypotheses to account for our results and discuss the importance of differences in age and language background as well as methodological parameters, a well-known challenge in research with young children. Further research is needed to develop robust tasks and to better understand the developmental trajectory of NAD processing abilities.