Have you considered a slight change of career? Perhaps a technical sales rep, or technical service engineer or some such thing that must be bilingual (French/English). Have you looked at the linked in group “French Connections”? There are other French groups on LinkedIn related to engineering, medical instruments, etc. It occurs to me that there must be some company that needs to send someone to France on service/consulting calls AND needs that person to be French speaking. Most folks would hate that kind of assignment because it would take them away from their families for weeks at a time. But it might be just right for you.
I too have been trying to find a job (but permanent) in France and move there (but with my wife and kids). My kids go to the French schools in San Diego. Unfortunately, although I speak some French, I am by no means fluent, and there seem to be plenty of smart software engineers that are fluent in French.
Anyhow, good luck to you. I am American but I love France. I particularly liked the Dordogne region.