[Curmudgeon]

The British of Bonaparte-7 can well afford to laugh.

In RLT (real-life timeline), the first successful sea-going steamship, as opposed to steamboat was Richard Wright's Experiment built by a British company in 1813. The first steamship, and first iron steamship, to actually put to sea was also British, the Aaron Manby and did so in 1822. The first steamship to cross the Atlantic is a little less clear. The American S.S. Savannah was technically the first, but made the voyage under sail; the British-built Cuacao made the crossing substantially using steam power in 1827; and the Canadian-built Royal William made the crossing in 1833, with sail being used only when the boilers were being maintained. Finally, the first steamship to use a screw propeller, instead of a paddlewheel, was the British-built SS Archimedes in 1839.

What Napoleon might make use of is steamboats. Even there, the French will be playing catch-up. Robert Fulton was inspired by the successful trials of the British-built SS Charlotte Dundas in 1803. In 1785, Patrick Miller had proposed a steam warship and presented a 100' small-scale version, Experiment to Gustav XIII of Sweden, though nothing came of it. The French had had a steamboat enthusiast, the Marquis de Jouffray, but he left France during the Revolution and the French effectively abandoned further work on steamboats.

The best bet for what you envision is a timeline where de Jouffray does not run out of funds and does not abandon France. Britain and France will probably end up in a steam arms race, with both sides achieving parity, but it's a less lop-sided proposition than Napoleon taking on a technologically superior Britain in a steam war.