In the majority of languages, the functional distinction between functors and content words correlates with lower-level, perceptually observable properties. Functors are generally more frequent and prosodically more minimal than content words. Previous studies demonstrate that the frequency distribution and the different acoustic realization of frequent and infrequent words guide infants in discovering their native word order. However, whether and if yes, how the exact frequency ratio impacts infants' ability to recognize function and content words and their relative order has never been explored. Here we investigate this by testing whether with a small ratio between functors' and content words' frequency, 1:3 as opposed to the 1:9 ratio in previous studies, French 8-month-olds are able to establish the functor-initial word order typical of their native language (Experiment 1) and whether prosody (Experiment 2) and the amount of exposure (Experiment 3) modulate this ability. We observed that infants exhibited the predicted functor-initial preference only when they were exposed to a short familiarization phase, i.e. reduced exposure. This suggests that different amounts of information selectively trigger different processing mechanisms, and little exposure may favor the extraction of regularities.