Hi,
I'm a GMAT teacher and MBA Coach in France, so I can shed a bit of light on this debate, as I've had many hundreds of students specifically seeking to study in the French market. To begin with EMLYON, as far as I understand, it was once viewed as one of the better MBA institutions in France, just after INSEAD and HEC, but has now fallen out of favor. To be frank, I have not had a single student apply to EMLYON in the last year. Though ESSEC is still on the lips of many individuals, but the school has a predatory approach to its ranking (e.g., forcing students to validate their years by taking the GMAT to receive higher scores). As for French, while it might be nice to know, I believe both MBA programs are taught in English.
If you're looking to work in France, HEC or INSEAD might be better bets. What are your metrics? Are you pursuing this degree straight out of school? Did you complete the GMAT or GRE?