Well, as Ive said in that othe rthread, Adenauer seemed to have an anti-east-germanyism complex or something, which is why Rhenish Republic or West German Republic both suited him fine...hes in that a special case, but in another way hes quite typical: As Lord Mayor of Cologne, he did look out for the welfare of his people, of course, and theres a point in that being easier when the occupation troops are not hostile to the current administrative buildup... I think Adenauer wouldve tried to arrange himself with the French to the point of accepting a Rhenish Republic, and so would have others, but thats of course quite something different from agitation for a Rhenish Republic, from a real movement. And I do think the number of people whod be ready to arrange themselves would be rather slim.
The real movement was indeed just French puppets, and just a tiny amount of them. Some people would indeed have accepted a Rhenish Republic to better the econimcial situation, due to the occupation troops then not being hostile anymore - that this would case is a rather easy conclusion to make, after all. I just dont think it would have been all that many.
As for long - for as long as the French would have propped up the puppet government. Which would indeed depend on the government in charge in France, but I cant see the Popular front investing many ressources on that. Especially not with Britain facepalming and muttering how fucking stupid this all is

And with how the country would have to be run undemocratically, basically, probably under some petexts of constantly shifting elections or somesuch... Maybe a leftist French government wouldnt let the Rhenish puppet government outright fall, but would gradually witdhraw support until it collapses...