Potentially, it might serve to draw the americans into the wider Napoleonic wars. My knowledge of American political attitudes in this era is sketchy, but if this happens it must mean the US has abandoned its earlier decision to not get entangled in european politics, what was the political POD here? Secondly, IIRC the US had a more favourable attitude to the French, add to this the British practice of stopping American ships to look for deserters etc, it seems plausible that the US may well throw their lot in with Napoleon.
The butterflys now take flight en masse
Would the wars widen to the americas?
Would the battle of Trafalgar still take place and be as favourable to the British?
Would the Peninsular army still go the peninsular, or would it end up in Canada?
I dont think that on balance the outcome would be that favourable to the US, at this stage in history if Britain is determined enough and commits the manpower and resources the US is in deep trouble. In the war of 1812 OTL, Britain was distracted and didnt particularly want a serious war in the Americas. Again, IIRC this war was a draw, with both sides exercising a degree of maturity and deciding that a negotiated settlement would pave the way for centuries of good relations between the US and GB.
If the US is allied with France, attitudes may very well harden on both sides. If GB wins and imposes a harsh peace treaty on the US, then the Americans may well look to rebuild their power base and get more actively involved in Eurpoean politics, initially as a minor player, but gradually becoming a more important player as the 19h century draws to a close.
With a non-isolationist and annoyed US, anything is possible at this stage.
A US/GB naval race. American participation in the carve up of Africa. A greater desire to formally dominate the Pacific and stop other european powers getting it first. This could lead to clashes with Fance, Germany, Russia (in Alaska) and GB.
Would the ACW still happen, would other powers be drawn into it. What if GB supported the rebs, would France declare war on GB in support of America? Would Bismarck use this as an oppurtunity to widen Prussian control in Germany? Would Austria stand for this? Would the Ottomans seize the oppurtunity to pick up a few african provinces? Would Russia use the oppurtunity to make a grab for Constantinople?
Imagine a series of wars all loosely connected with other, the sides being roughly US/France/Austria/Russia vs GB/Prussia/CSA/Ottomans.
Anyway, i'll stop there (maybe i should go away and write this TL
).
My main stumbling block is a - the US getting entangled in Africa at this stage and b - their ability to project sufficient force to make it a reality.