So I was wondering if France had stumbled, say in the face of England or Spain, would an Austria free of French intervention be able to consolidate power and reform the HRE into a more centralized nation state?
Protestantism killed the HRE not France.
France in her infinite kindness only freed the catatonic corpse of its hellish existence.
France had little to do in the conflict with the pope. The only time where France intervention was major was in the 30 HYW which was the cause of the HRE's cancer: protestantism.
So I was wondering if France had stumbled, say in the face of England or Spain, would an Austria free of French intervention be able to consolidate power and reform the HRE into a more centralized nation state?
Right. France was a relatively week power until the end of the Hundred Years War. The conflict with the Habsburgs that developed afterwards took place mainly in Italy where it could find local allies, it didn't attempt anything big on the northern front. After the Reformation, France was equally hampered by internal division but it recovered earlier, finally allowing it to meddle in Germany itself.Again during the Emperor-Pope conflict France was absent. France had nothing to do with the failure of Frederick II to defeat the Lombards League for exemple.
France had her own problem to deal with during that period with her own unruly vassals like a certain King of England and others and it was the Emperor who was intervening in France not the reverse.
Also I don't see how the Ottomans were not a menace were they besieged the freaking capital twice and the city was saved by foreign intervention two times too.
It seems following the peace of Whestphalia the Habsburgs directed less and less effort towards the Empire although the treaty itself merely confirmed the Status quo between the Emperor and the Princes and did not constitute any radical Change. Much more important was weakness of Spain and the rise of France as the new dominant power in Europe.
Identities are forged and not a given. I think you underestimate how long the Habsburgs, Romanovs and Ottomans dominated vast and diverse Empires all of which were much more centralized than the HRE. A successfull centralization of the Empire was not dependent on giving up any parts of the Empire it was dependent on achieving stability and a Balance of power that was favourable to the Emperor.
Even before protestantism, it didn't gone well in the Empire: too powerful stem dukes who achieved to get the hereditary of their charges (IIRC, the Empire become a feudal empire under Frederic the First) but quite rarely acted in the interest of the Empire; strong hostility from the pope who decided to be an higher authority than the emperor who get to be elected without the approval of the emperor; in early time suspicions between stem nations; suspicions between stem nations and italian nation; some good emperors who died too young; coherencies of policies between emperors who had to negotiate terms of their election with electors...France had little to do in the conflict with the pope. The only time where France intervention was major was in the 30 HYW which was the cause of the HRE's cancer: protestantism.