While the Americans might applaud a coup that gets rid of socialist that could have seemed to be opening the door to socialist revolution, these days they would have expected a fairly rapid return to democracy, i.e. Levarge could have possibly served out Josephus' term, but would have had to let the next election proceed, although perhaps the ESA could have been banned from running candidates. Levarge could of course run in that election, probably against O'Floinn, unless Loic could have re-entered the country by then. Loic more likely would have been in charge of PFLU, Provinces Francophone Libres Unies, i.e. a break-away Nouvelle Anjou and Nouvelle Acquitaine, perhaps including St. Esprit within a (necessarily) loose confederation.
If the US thought that Josephus might only be a one term wonder, with no danger of a socialist revolution taking hold, then they would have been extremely hesitant to back your coup. Thus, the only time that they might have backed you coup was during or right after the million man march.