Question: The Treaty of Fontainebleau was signed by which ruler of the Habsburgs from 1780-90?

Context paragraphs:
Treaty of Fontainebleau (1745): The Treaty of Fontainebleau was signed on October 24, 1745 in Fontainebleau, France between Louis XV of France and the pretender to the thrones of Great Britain and Ireland, Charles Edward Stuart.  Based on the terms of the accord, both signatories agreed to establish a military alliance against George II of Great Britain who was also the Elector of Hanover.

Treaty of Hamburg (1638): The Treaty of Hamburg was signed in Hamburg in 1638 by Cardinal Richelieu of France and representatives of Queen Christina of Sweden.  Based on the terms of the treaty, France paid Sweden 1,000,000 livres for its military contributions against the Habsburgs.  Moreover, the accord confirmed their alliance set by the tenets of the Treaty of Wismar.

Treaty of Fontainebleau (1631): The Treaty of Fontainebleau (German: "Vertrag von Fontainebleau" ) was signed on May 30, 1631 between Maximilian I, Elector of Bavaria, and the Kingdom of France.  The accord established a secret alliance between the two Catholic states during the Thirty Years' War.

Treaty of Fontainebleau: The Treaty of Fontainebleau refers to a number of agreements signed at Fontainebleau, France, often at the Château de Fontainebleau:

Treaty of Copenhagen (1670): The Treaty of Copenhagen or Treaty of 1670 was a treaty of commerce and alliance signed on July 11, 1670, between King Christian V of Denmark and of Norway and King Charles II of England and of Scots.  It was written in Latin.  It was expanded the next day on July 12, 1670, with the Third Article concerning contraband amended and clarified by a declaration in French signed at Copenhagen on July 4, 1780.  The terms of the treaty were later reaffirmed by the Treaty of Kiel, following the defeat of Denmark-Norway during the Napoleonic Wars.

Treaty of Fontainebleau (1807): The Treaty of Fontainebleau was a secret agreement signed on 27 October 1807 in Fontainebleau, France between King Charles IV of Spain and the French Emperor Napoleon.  Under the treaty, the House of Braganza was to be driven from the Kingdom of Portugal with the country subsequently divided into three regions.

Kingdom of Sardinia (1700–1720): From 1700 to 1720, the Kingdom of Sardinia, as a part of the Spanish empire, was disputed between two dynasties, the Habsburgs and the Bourbons.  With the death of Charles II, the last of the Spanish Habsburgs, on 1 November 1700, the throne passed to Duke Philip of Anjou (Philip V), although the Emperor Leopold I also had a claim.  Leopold was especially desirous of obtaining the Spanish inheritance in the Southern Netherlands and in Italy, which included Sardinia.  With the failure of France to abide by the Second Partition Treaty, the other European powers lined up on the side of the Habsburgs.  The Treaty of the Hague (7 September 1701) allotted to the Emperor the Spanish possessions in Italy.  Imperial troops invaded Italy to seize them, and the War of the Spanish Succession began.

Treaty of Fontainebleau (1814): The Treaty of Fontainebleau was an agreement established in Fontainebleau, France, on 11 April 1814 between Napoleon I and representatives from the Austrian Empire, Russia and Prussia.  The treaty was signed at Paris on 11 April by the plenipotentiaries of both sides and ratified by Napoleon on 13 April.  With this treaty, the allies ended Napoleon's rule as emperor of France and sent him into exile on Elba.

Joseph II, Holy Roman Emperor: Joseph II (Joseph Benedikt Anton Michael Adam; 13 March 1741 – 20 February 1790) was Holy Roman Emperor from 1765 to 1790 and ruler of the Habsburg lands from 1780 to 1790.  He was the eldest son of Empress Maria Theresa and her husband, Emperor Francis I, and was the brother of Marie Antoinette.  He was thus the first ruler in the Austrian dominions of the House of Lorraine, styled Habsburg-Lorraine.  Joseph was a proponent of enlightened absolutism; however, his commitment to modernizing reforms subsequently engendered significant opposition, which eventually culminated in an ultimate failure to fully implement his programmes.  He has been ranked, with Catherine the Great of Russia and Frederick the Great of Prussia, as one of the three great Enlightenment monarchs.  His policies are now known as Josephinism.  He died with no sons and was succeeded by his younger brother, Leopold II.

Treaty of Fontainebleau (1785): The Treaty of Fontainebleau was signed on November 8, 1785 in Fontainebleau between Holy Roman Emperor Joseph II, ruler of the Habsburg Monarchy, and the States-General of the United Provinces.  Based on the terms of the accord, the United Provinces was permitted to maintain sovereignty over the Scheldt Estuary.  However, it had to provide several concessions to the Habsburgs including payment of ten million Dutch florins and dismemberment of certain military fortifications.  Overall, the treaty confirmed and reinforced the tenets of the Treaty of Münster.

Supporting paragraphs: Treaty of Fontainebleau (1785) Joseph II, Holy Roman Emperor
Answer: Joseph II