Tough situation, and you need to speak with an attorney.
First, you can't apply for a fiance visa for him when you are a permanent resident (only a citizen can apply). also, the process for a spouse of a permanent resident is very long.
On the other hand, being illegally in France doesn't impact his legal status in the U.S.
Question is, can YOU get U.S. citizenship? May make the most sense for you to apply to naturalize as a citizen, and then apply for a fiance visa or green card for him (which wouldn't then take as long).
Whole thing would be in the neighborhood of a year and a half, instead of many years. Not great, but possible.
Speak with a lawyer for further guidance.