I used "i.e." to signify the countries that best represented that attribute. I obviously did not include every single European power. France was indifferent to the Austrian Succession. France was unwilling to commit to a major war against Austria since Spain (France's main ally) was occupied with Britain, the Ottomans (another French ally) were recently defeated, Sardinia was completely unreliable, and the German States for the most part were initially supportive of Maria Theresa. Instead France offered vague guarantees of support to Austria but had no intention of fighting to defend Austria in the event that a war broke out. It was only the fact that Austria was shockingly defeated by Prussia that convinced France to sponsor and fund Maria Theresa's enemies.
Austria did not do almost nothing. They immediately rejected the Prussian proposal and began to regroup their Silesian forces and raise more armies. The reason they did not immediately launch a counterattack was because Frederick II, wisely, attacked so late in the campaign season that Austria could not launch a counterattack yet. Furthermore another reason the Austrians did not quickly launch a counterattack was because there were two competing plans for the counterattack and Maria Theresa had to decide which one she wanted.
Frederick II would not have backdowned. He was confident in the ability of the Prussian army and had entrenched himself in Lower Silesia. He had deliberately crossed the Austrians and was fully aware of the potential consequences. That is why when the Austrians denied his proposal the first thing he did was open negotiations with the French to secure their support.