A Napoleonic Empire map
This is a map that a cooked up. I don't have a detailed timeline but the POD is that Kutuzov persuades the Tsar and Austrian Emperor to avoid battle with Napoleon at Austerlitz. Prussia joins the 3rd Coalition against Napoleon in early 1806, and Napoleon is unable to decisively defeat all 3 powers at once. He makes peace with them, and with Britain about a year later. He decides that Britain is the greatest enemy, and begins a program to build up France's navy, industry, and colonies to compete with Britain. The 19th century that follows is a long colonial and naval rivalry between Britain and France. Ironically, Russia and France end up as (sort of) allies because of their common rivalry with Britain.
With most of Germany and Italy still divided up between small states that are dominated by France, there is no successful unification movement in either country. Prussia and Austria remain major powers, but Austria survives nationalist pressures by decentralizing into a more federal structure in the late 19th century.
The Ottoman Empire is friendly with Britain, but has lost quite a bit of territory in the Balkans to Russia. Egypt is still nominally part of the Ottoman Empire, but is virtually a separate state that is dominated by France.
China is nominally independent but is totally divided between Russian, British, and French spheres of influence. Japan was forced open by the western powers a little earlier, but failed to modernize. It too is nominally independent, but divided into Russian and French spheres of influence.
The French established bases in western Australia around 1820. The British were outraged, but not prepared to go to war over the issue. Australia ended up split between the British and French
The US gets more territory from Mexico but settles for the Columbia river as the boundary in the northwest. The US Civil war occurs in the late 1850s instead of the early 1860s. The Confederacy establishes its independence with French aid, while Britain remains neutral. The Confederacy is still friendly to France, while the US has grown closer to Britain.