The issue with Fultons Catamaran designs is that they were only really meant for coastal use, they'd be great for defending the French against raids, but without some serious design changes, they'd be less effective against British Ships in open water.
Even if they were adapted for deep water, if they were anything like Fultons designs IOTL, they may have had wind-independence, but when there is a wind, sailing ships can outrun them, and circumvent them.
Combine the risks of having the steam boiler on a ship with a gunpowder store, that could increase the chance of the ship being destroyed, and its limited advantages, I'm doubtful Napoleon would use them.
HOWEVER - that said, lets assume Napoleon does build some - I'm not sure he'd have any great advantage with them, unless he focused on using them as combined sail-ships. Give them a sail to give them a more typical speed, and then when needed, have them drastically alter course, ramming ships with a specialised hull - that would seriously mess up British battle strategies.
So potentially the French may think of Fulton as an innovative scientist, who helped Napoleon control the seas, and Napoleon could increase his chances of enforcing the Continental System. If we take this further, because there was impressive success, then after expanding these forces for Napoleon, Fulton may end up inadvertently helping the Americans if they still attempt to invade Canada whilst Britain's Navy is getting battered. (Arguably, with their abilities proven in battle, or popular, the Americans may well build some of these models themselves). With weaker logistics, the British will have a harder time supplying themselves in Canada.
An interesting possibility would be that if Napoleon is confident that he could project power across the ocean, he could work with the Americans - taking Quebec, in exchange for assistance in any invasion of Canada. The Quebecois are happy, the Americans get more strength (due to American ingenuity) and Britain gets a bloody nose.
Admittedly, in the short term, Napoleon is going to have to redirect resources, but if a successful hybrid is made - and the British are unable to duplicate them - in the long term Napoleon can transform his navy - he just needs to ensure he has enough wood and coal to power the ships.
TL;DR - Give him a fast ship, and an impressive victory or three, and you could see the Naval war change. He may still invade Russia though, which no amount of steamships are going to help with.
