(Note: I'm Hungarian, so there can be mistakes in the text, please excuse it me :))
In this althist the Ottomans won Siege of Eger in 1552, and during the next years they conquered Hungary and the Habsburg Empire. With destroying the defenders of Christianity, the way opened to Europe, and the western world ...
Points of divergence
1466 AD: Columbus discovers the Americas earlier, so the colonizing of them also starts before OTL.
1530 AD: Emperor Ferdinand I of the Austrian Empire gets the throne of Spain and it becomes the part of the Habsburg Empire.
The alternative history starts at it’s PoD, the end of the siege of Eger. After the victory in 1552, Suleiman, the sultan of the Ottoman Empire started a campaign against Hungary, and the whole Habsburg Empire. By 1554 the empire took the control over Vienna and Bratislava. To save his country, Ferdinand I (1526-1554) sent a sue for peace to Suleiman, but in August, he dead at the Siege of Graz. The Habsburg family tried to find a new heir, but the high-powers of Europe declared war on Austria. The War of the Habsburg Succession started in 1556, but until the conflict, the Ottomans conquered Austria, and the Habsburg Empire collapsed. In 1560, after the Peace of Vienna, the Ottomans took Hungary and Austria. Spain elected a new king, France acquired provinces in Bohemia, Netherlands declared independence, and the Holy Roman Empire collapsed. In the next century Ottomans continued the conquests in Europe, and they became an important part of the European politics. A key event was the alliance between the Ottomans and the Christian state Poland in he war against Lithuania, which ended the victory of Poland. The Ottomans got estates in North Europe, and the West European community disinherited the Polish country. This event led to the Ottoman-French War from 1683 to 1692. The Ottoman army destroyed the French at Poitiers, and the Turks got the eastern provinces of France under the Peace of Strasbourg. Meanwhile, the English parliament confronted with the king, Jacob I in 1688. One year later the First English Revolution broke out, but the king with his Portuguese allies crushed the rebels.
Fall of France
After the peace of Strasbourg, France lost its prestige, and became bad known. Ottomans created a military area around the French border, and they were preparing for a possible war in Western Europe. In 1711 the nearby countries, like Naples, Spain and England allied each other, and declared war on France. The armies of the Alliance invaded France from three directions. Until 1718 they conquered most of France, and the king escaped from the country. During the war the idea of the enlightenment started to arise in the West. First time English philosophers talked about the freedom of religion, speech and press. The new ideas led to the Second English Revolution, which later became a civil war. The British armies in France returned to the motherland but therefore, they lost some conquered territories in the hostile land. The king, George III, cannot protect his country against the rebels, who claimed the republic. Finally, the Rebels conquered London, executed the king, and proclaimed the Republic of Great Britain in 1721. In 1722, the Ottoman Empire started the war against France, and invaded some territories of the kingdom. In the next years Great Britain returned to the war, and protected its territories against the Ottoman campaign. In 1725 the war ended with the Peace of Versailles, which contained the British annexation of France, and gave the colonies to Naples and Spain.
West and East