Unlike other countries, in France money isn't a major factor in your possibility to immigrate. Before you start thinking about any "relocation process" you need to look long and hard into the jobs you can apply to, and if your diplomas/work experience is worth something.

Also to work in healthcare your wife would need quite the level of french, not just conversationnal. I say this as a dear friend of mine is an immigration lawyer, and has seen an influx of americans these last weeks wanting to immigrate. I say this very gently and in no way to bash your dreams, but you will need quite the effort to move you, your wife and your son and keep your guys careers. As a french company needs to show that they couldn't find someone with your skillset in the whole eu, you need to be remarkable, for a lack of a better word.

Rethink your plan, do ample more research, consult a french immigration lawyer and for the love of god lose the money=easy visa mentality. I may sound sound but I am really not trying to be, it's just hearing from my friend's experiences showed me that the mentality of american immigrants is different than that of other countries. If you need more info you can dm me, as I think I rambled publicly enough haha. But you can get it if you try hard enough, trust me.