I don't think professionals are all on the same page with ADHD vs. Aspergers. And some kids are iffy. It seems that France does not really like to diagnose kids with anything. In the US, who knows what diagnosis. J would have? in my opinion it doesn't matter as long as the child is getting the necessary help.
Autism Spectrum Disorders (ASD) and ADHD, if they are not on the same spectrum, both do lead to executive function disorders and this is a difficult problem. This link explains executive function problems in ADHD and Autism Spectrum Disorders (ASD). Of course, kids don't usually have EVERYTHING symptom.
http://www.milestonemom.com/how-to-promote-executive-function-in-children-with-adhd-autism-and-learning-disabilities/