If he goes it will be more like a consensus imo....both sides not thoroughly happy. Without full support from the board (and that has been strangely absent), why would Puel want to stay....it can be incredibly hard to regain the fans' support. He would have to be sure that his plans will succeed next season. Why would you put yourself through that if another job is possible.
Sorry , He is a top manager IMHO . When he left us , I heard he was VERY well respected by the club employees & Players .
I was gutted when he left but that was a long, long time ago. But now? God no... He's also a bit of a ****
St. Etienne would be a massive drop down from Saints. They were one of the leading French teams in the 1970's but got eclipsed by Lyon in the 1990's. I don't think it is accurate to see them as one of the "great" clubs in French football any more and they are probably comparable to Nice or Lille where Puel previously managed. I believe it is a former coal mining town and in lacking glamour. I have never been there. There have a great league pedigree but it is all historic. I suppose, it is the kind of equivalent of an English team like Villa.
From my limited knowledge of French football, I think your analogy is sound. But then the challenge of re-building a club might appeal. I want Claude to stay, but if he goes because he wants to go back to France I would get that. I know a few French people who have lived in the UK, and wanted to get back to France after a time. I know others who have settled, but there is little question that (to parody L P Hartley) France is a foreign country: they do things differently there.
Harry takes first place in my list of managers who I absolutely do not want. Pearson is second. The two of them are far, far ahead of anyone else.