We report the results of an empirical study which aims to describe the discourse function of rises at right edge intonation boundaries in French. A Map-Task corpus containing two dialogues was annotated for IP boundaries and pitch transition points with the INTSINT intonational alphabet. The transcripts of the dialogues were labeled for dialogue structure and dialogue acts, using form and function tags. The relation between rises at IP boundaries with types of dialogue acts and topic shifts was statistically evaluated. As expected, the results show a positive correlation between rises and polar questions and between rises and discourse topic openings. Interestingly, the second correlation was stronger than the first, suggesting that the association of rises with topic openings is not simply due to the effect of questions as introducing new topics.