This work is based on previous studies showing that a short conversational intervention (SCI) focusing on the causes of the story events is effective in promoting the causal and mental content of children’s narratives. In these studies, however, not all the children improved their narratives after the SCI). The present study examined individual differences in the effectiveness of the SCI and investigated whether they were related to variation in the children’s executive function skills such as cognitive inhibition and flexibility. Eighty 6- to 8-year-old French-speaking children participated in the narrative task and executive function tasks. In the narrative task, they first told a story (NAR1) based on the Stone Story made up of five wordless pictures involving a misunderstanding between two characters; each child then participated in the SCI, and finally narrated the story a second time (NAR2). Then, the children were presented with executive function tasks. Cognitive inhibition was assessed by the Animal Stroop test, and cognitive flexibility was assessed by a three-criterion classification task and a local/global figure-matching task. Group results showed that the children expressed the misunderstanding between the characters in mental terms significantly more in their second than in their first narratives. Results also showed individual variation in the post-SCI improvements and indicated a significant positive relation between large improvements in the children’s post-SCI narrative and their inhibitory control skills. No significant relations were found in this study between large improvements and the two cognitive flexibility measures. These results suggest that narrative-promoting interventions should closely consider individual differences in the effectiveness of their procedures and envisage working not only on promoting narrative content but also on the skills needed to benefit from the interventions.