Outside of Joseph II and Leopold II, who wanted to see how events would play out before taking any action and didn't live to see the end of the French monarchy in 1792, were there any other members of the Austrian Habsburgs who tried to help Marie Antoinette in some capacity?
Although Francis II was reported to have been indifferent to Marie Antoinette, was there any pressure from his surviving aunts and uncles to help her and her family? In addition, were there other members who wanted to save her? And did they make an effort to do so? If not, what was stopping them?
Attempts by the Hapsburg Monarchy and their fellow sovereigns to safeguard Louis XVI and Marie Antoinette were actually one of the main causes of the outbreak of the French Revolutionary wars. After Louis and Marie were captured trying to flee France in the summer of 1791, Leopold II and Frederick William II of Prussia issued the Declaration of Pillnitz, stating that the sovereigns of Europe would go to war with France if the King and Queen were harmed.
This didn't help. While the declaration was carefully crafted to only state that Austria would only go to war as part of a general European alliance, it was interpreted in France as a statement of intent towards war. This galvanised the pro-war party within the National Assembly and further damaged the standing of the King and Queen; Marie Antoinette in particular had already been seen as an Austrian interloper, and the Declaration only heightened this perception. The outbreak of war with Austria in 1792 resulted in a series of French defeats, and the idea that Austrian and Prussian troops would march on Paris led to a variety of riots, including the storming of the Tuilieries Palace which finally broke what little authority the monarchy had been able to hold onto. The formal end to the monarchy, and the execution of Louis and Marie, would follow in the next six months.
To answer your second question: France was already at war with the Hapsburg Empire. helping the royal family would have required the capture of Paris, which was made impossible by a French victory at Valmy in September. There wasn't really much more the Austrians could do.