What do "mention", "promotion", and "situation within your promotion" mean in this paragraph describing a CV?
This sounds like a bad translation from French (and it's not unlikely that the coordinator has no clue how to explain what these terms mean).

The French "promotion" means "promotion", but also "class" or "cohort". "Mention très bien" is an exam passed with "distinction". "Situation" means "situation" but also "position". So what they probably want is: 


  CV outlining the following information: exams passed with distinction, rank of classification, position within your class/year/cohort, number of students in the class/year/cohort, diplomas with indication of specialty, date of graduation, any special distinction/honors and final marks certified by the institution.