A basic constituent of French intonation is the Accentual Phrase (AP), which includes two distinct tonal events: a final LH* accentual rise and an initial LHi rise. A previous study had shown a difference between the rising movements according to the the position of the AP within the intonational phrase (IP): prenuclear (P, IP-initial) versus nuclear (N, IPfinal). The present paper explains this difference through the occurrence of a LHi in P position which does not occur in N position. Specifically, we tested whether LHi can occur adjacent to LH* within the AP and whether the occurrence of LHi triggers initial strengthening of the onset consonant independent of its status (as a liaison consonant or not). Four native speakers of French read target words varying as to their distribution within the intonation phrase as well as to the segmental nature of the target syllable onset (/k/ onset versus /z/ liaison). Results confirm that LHi can be immediately adjacent to LH* within the AP, but only in P position and that the height of its H target is influenced by onset consonant type. The results are discuss relative to the phonological status of the initial rise and the phonological structure of the nuclear pitch accent in our data.