What are my chances of getting into McKinsey/BCG France as a non-target student?

I'm currently an engineering student in France, doing a specialized Masters in Chemical and Process Engineering and simultaneously working as an engineer (in Oil&Gas) as part of a co-op/apprenticeship arrangement. While I'm set to graduate and enter the workforce next summer, I had a slight change of heart concerning my future career ambitions and I gradually realized (after intense research on diverse avenues of employment) that Management Consulting is better suited for my personality and aligns with the type of work I'd like to be doing (multifaceted, dynamic, not as pigeonholed as most engineering roles). 
Furthermore, France is a hotbed for some of the biggest names in consulting, notably the ones in my topic title. So I was wondering what the entry opportunities are for someone who isn't from a target school (one of the big name business schools in the country such as HEC, ESSEC, etc.). I know that the vast majority of employees come from these schools but I was wondering if someone who followed a more nontraditional path could share their experience and how they got there (if such people even exist, the French are notorious for being very rigid in certain hiring practices and placing great value on status symbols and signals such as the name of your school). Would be happy to provide any further info if it helps with clarifying whether I'm a good fit.